Dear Anton,
sorry for troubling you again.
so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
Best,
Camilla
The code if needed:
import kwant import tinyarray as ta import numpy as np from scipy import sparse from matplotlib import pyplot import matplotlib
s0 = ta.array([[1, 0], [0, 1]]) sx = ta.array([[0, 1], [1, 0]]) sy = ta.array([[0, 1j], [-1j, 0]]) sz = ta.array([[1, 0], [0, -1]])
# Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2
def make_system(t=1.0, W=10, L=10): # Now we must specify the number of orbitals per site. lat = kwant.lattice.square(norbs=2) syst = kwant.Builder()
syst[(lat(x, y) for x in range(L) for y in range(W))] = \ lambda s, alpha, E_z: 4 * t * s0 + E_z * sz syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx
# The new bit: specifying the conservation law. lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law=-sz, time_reversal=s0) lead[(lat(0, j) for j in range(W))] = 4 * t * s0 lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead.
syst.attach_lead(lead) syst.attach_lead(lead.reversed())
syst = syst.finalized()
return syst
syst = make_system(t=1.0, W=10, L=10) energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in energies]
fig = pyplot.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1)
# Like previously smatrix.transmission(lead1, lead0) is transmission from lead0 to lead1 ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices], label='total')
# The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the transmission from the # q0 block of the lead0 into the q1 block of lead1. The subblock ordering is same as we used # in set_symmetry. ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in smatrices], label='$G_{↑↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in smatrices], label='$G_{↑↓}$') ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in smatrices], label='$G_{↓↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in smatrices], label='$G_{↓↓}$') ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large');
On 24. jan. 2017 13:18, Anton Akhmerov wrote:
OK, please double-check the remaining simulation parameters.
Anton
On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
I triend changing it, but that does not solve the problem.
Best,
Camilla
From: Anton Akhmerov [mailto:anton.akhmerov+kd@gmail.com] Sent: 24. januar 2017 12:36
To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
Could the difference originate from you using a lattice constant of 2 instead of 1?
Anton
On Tue, Jan 24, 2017, 10:41 Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
Thanks again for all your help. I will try to do it the linux way. Just one more thing regarding this. I wrote a script in the old Kwant to find the total conductance and compare it to the one in your notebook. While the two plots are qualitatively similar, they are not the same. Am I missing something, or am I calculating different things?
Best, Camilla
(my code):
# Tutorial 2.3.1. Matrix structure of on-site and hopping elements # ================================================================ # # Physics background # ------------------ # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng, # as theoretically predicted in # http://prl.aps.org/abstract/PRL/v90/i25/e256601 # and (supposedly) experimentally oberved in # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html # # Kwant features highlighted # -------------------------- # - Numpy matrices as values in Builder
import kwant
# For plotting import matplotlib.pyplot as plt
# For matrix support import tinyarray import numpy as np
# define Pauli-matrices for convenience sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, 1j], [-1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])
def make_system(a=2, t=1.0, alpha=0.1, e_z=0.05, W=10, L=10): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity). lat = kwant.lattice.square(a)
sys = kwant.Builder()
#### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x
#### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0)))
lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 # hoppings in x-direction lead[lat.neighbors()] = \ -t * sigma_0
#### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed())
return sys
def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(1, 0))
pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show()
def main(): sys = make_system()
# Check that the system looks as intended. kwant.plot(sys)
# Finalize the system. sys = sys.finalized() energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(sys, energy) for energy in energies]
fig = plt.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1)
ax.plot(energies, [smatrix.transmission(1,0) for smatrix in smatrices], label='total')
ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large')
plt.show()
# Call the main function if the script gets executed (as opposed to imported). # See http://docs.python.org/library/__main__.html. if __name__ == '__main__': main()
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 17. januar 2017 10:48 To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
It seems that you are trying to install Kwant on windows. This is a very hard task, and I fear none of the Kwant developers has enough knowledge of it right now (our Windows packages are built by Christoph Gohlke, see [1] for the build environment description). However if you are using windows 10, I suggest to try to install Kwant using the windows subsystem for linux. That way the standard Ubuntu build procedure should work for you.
Best, Anton
[1]: http://www.lfd.uci.edu/~gohlke/pythonlibs/
On Mon, Jan 16, 2017 at 9:45 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Thanks a lot. I tried to install the cons_laws_combined, but I get the following error message:
"LINK: fatal error LNK1181: cannot open input file 'lapack.lib'"
Is there some package or installation I am missing?
Best regards, Camilla
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 8. januar 2017 16:35 To: Tómas Örn Rosdahl torosdahl@gmail.com Cc: Camilla Espedal camilla.espedal@ntnu.no; kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Hi Camilla, everyone,
I've slightly modified Tómas's example to a case where the spins do get coupled, check it out: http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductanc e.ipynb
I've also provided more detailed installation instructions in the notebook.
Cheers, Anton
On Sun, Jan 8, 2017 at 2:45 PM, Tómas Örn Rosdahl torosdahl@gmail.com wrote:
Dear Camilla,
For a Hamiltonian with degeneracies due to a conservation law, the scattering states will in general not have a definite value of the conservation law. In your case, Kwant returns scattering states that are arbitrary linear combinations of spin up and down, so it is not possible to label the amplitudes in the scattering matrix by spin.
However, in Kwant 1.3 a feature will be added that allows for the construction of scattering states with definite values of a conservation law. See here for an explanation of the basic idea behind the algorithm.
We're currently working on implementing this feature in Kwant itself. The good news is that we're practically done - here is a link to a git repo with a functioning implementation. After you clone the repo, check out the branch cons_laws_combined, which contains a version of Kwant with conservation laws implemented. This notebook contains a simple example to illustrate how to work with conservation laws and the scattering matrix.
I invite you and anyone else who is interested to give it a try. We'd appreciate any feedback!
In your case specifically, there would be two projectors in the new implementation - P0 which projects out the spin up block, and P1 that projects out the spin down block. If they are specified in this order, then the spin up and down blocks in the Hamiltonian have block indices 0 and 1, respectively. In the new implementation, it is possible to ask for subblocks of the scattering matrix relating not only any two leads, but also any two conservation law blocks in any leads. To get the reflection amplitude of an incident spin up electron from lead 0 into an outgoing spin down electron in lead 0, you could simply do smat.submatrix((0, 1), (0, 0)). Here, the arguments are tuples of indices (lead index, block index).
Best regards, Tómas
On Fri, Jan 6, 2017 at 3:46 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Hi again,
This question is basically the same as this: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg0007 6 .html
I want to calculate some things using the scattering matrix. I started out with a very simple system, most basic two-terminal system. For some energy there is one propagating mode. I now add matrix structure to the mix (just multiply by s_0 everywhere) and there are now 2 propagating modes (which makes sense).
Now, if I look at the reflection coefficients for lead 0 by using submatrix(0,0), it is now a 2x2 matrix after I introduced the matrices. How are the elements ordered? Is it
[[r_upup, r_updown],[r_downup, r_downdown]]
I know that I could make two lattices, but since I do not plan to use the other functions such as transmission. I just want the smatrix.
Hope you can help me, and thanks in advance.
Best regards,
Camilla
Hi Camilla,
Sure. You need to install a development version of tinyarray. If you got everything via conda, then you can do " conda install -c kwant 'tinyarray==dev' ". If you installed kwant via pip, do " pip install git+https://gitlab.kwant-project.org/kwant/tinyarray.git@master "
Let me know if it works (both the installation and using the conservation laws).
Best, Anton
On Tue, Feb 14, 2017 at 9:40 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
sorry for troubling you again.
so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
Best,
Camilla
The code if needed:
import kwant import tinyarray as ta import numpy as np from scipy import sparse from matplotlib import pyplot import matplotlib
s0 = ta.array([[1, 0], [0, 1]]) sx = ta.array([[0, 1], [1, 0]]) sy = ta.array([[0, 1j], [-1j, 0]]) sz = ta.array([[1, 0], [0, -1]])
# Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2
def make_system(t=1.0, W=10, L=10): # Now we must specify the number of orbitals per site. lat = kwant.lattice.square(norbs=2) syst = kwant.Builder()
syst[(lat(x, y) for x in range(L) for y in range(W))] = \ lambda s, alpha, E_z: 4 * t * s0 + E_z * sz syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx # The new bit: specifying the conservation law. lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law=-sz, time_reversal=s0) lead[(lat(0, j) for j in range(W))] = 4 * t * s0 lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead. syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst
syst = make_system(t=1.0, W=10, L=10) energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in energies]
fig = pyplot.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1)
# Like previously smatrix.transmission(lead1, lead0) is transmission from lead0 to lead1 ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices], label='total')
# The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the transmission from the # q0 block of the lead0 into the q1 block of lead1. The subblock ordering is same as we used # in set_symmetry. ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in smatrices], label='$G_{↑↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in smatrices], label='$G_{↑↓}$') ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in smatrices], label='$G_{↓↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in smatrices], label='$G_{↓↓}$') ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large');
On 24. jan. 2017 13:18, Anton Akhmerov wrote:
OK, please double-check the remaining simulation parameters.
Anton
On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
I triend changing it, but that does not solve the problem.
Best,
Camilla
From: Anton Akhmerov [mailto:anton.akhmerov+kd@gmail.com] Sent: 24. januar 2017 12:36
To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
Could the difference originate from you using a lattice constant of 2 instead of 1?
Anton
On Tue, Jan 24, 2017, 10:41 Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
Thanks again for all your help. I will try to do it the linux way. Just one more thing regarding this. I wrote a script in the old Kwant to find the total conductance and compare it to the one in your notebook. While the two plots are qualitatively similar, they are not the same. Am I missing something, or am I calculating different things?
Best, Camilla
(my code):
# Tutorial 2.3.1. Matrix structure of on-site and hopping elements # ================================================================ # # Physics background # ------------------ # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng, # as theoretically predicted in # http://prl.aps.org/abstract/PRL/v90/i25/e256601 # and (supposedly) experimentally oberved in # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html # # Kwant features highlighted # -------------------------- # - Numpy matrices as values in Builder
import kwant
# For plotting import matplotlib.pyplot as plt
# For matrix support import tinyarray import numpy as np
# define Pauli-matrices for convenience sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, 1j], [-1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])
def make_system(a=2, t=1.0, alpha=0.1, e_z=0.05, W=10, L=10): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity). lat = kwant.lattice.square(a)
sys = kwant.Builder() #### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 # hoppings in x-direction lead[lat.neighbors()] = \ -t * sigma_0 #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys
def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(1, 0))
pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show()
def main(): sys = make_system()
# Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(sys, energy) for energy in energies] fig = plt.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1) ax.plot(energies, [smatrix.transmission(1,0) for smatrix in smatrices],
label='total')
ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large') plt.show()
# Call the main function if the script gets executed (as opposed to imported). # See http://docs.python.org/library/__main__.html. if __name__ == '__main__': main()
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 17. januar 2017 10:48 To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
It seems that you are trying to install Kwant on windows. This is a very hard task, and I fear none of the Kwant developers has enough knowledge of it right now (our Windows packages are built by Christoph Gohlke, see [1] for the build environment description). However if you are using windows 10, I suggest to try to install Kwant using the windows subsystem for linux. That way the standard Ubuntu build procedure should work for you.
Best, Anton
On Mon, Jan 16, 2017 at 9:45 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Thanks a lot. I tried to install the cons_laws_combined, but I get the following error message:
"LINK: fatal error LNK1181: cannot open input file 'lapack.lib'"
Is there some package or installation I am missing?
Best regards, Camilla
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 8. januar 2017 16:35 To: Tómas Örn Rosdahl torosdahl@gmail.com Cc: Camilla Espedal camilla.espedal@ntnu.no; kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Hi Camilla, everyone,
I've slightly modified Tómas's example to a case where the spins do get coupled, check it out: http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductanc e.ipynb
I've also provided more detailed installation instructions in the notebook.
Cheers, Anton
On Sun, Jan 8, 2017 at 2:45 PM, Tómas Örn Rosdahl torosdahl@gmail.com wrote:
Dear Camilla,
For a Hamiltonian with degeneracies due to a conservation law, the scattering states will in general not have a definite value of the conservation law. In your case, Kwant returns scattering states that are arbitrary linear combinations of spin up and down, so it is not possible to label the amplitudes in the scattering matrix by spin.
However, in Kwant 1.3 a feature will be added that allows for the construction of scattering states with definite values of a conservation law. See here for an explanation of the basic idea behind the algorithm.
We're currently working on implementing this feature in Kwant itself. The good news is that we're practically done - here is a link to a git repo with a functioning implementation. After you clone the repo, check out the branch cons_laws_combined, which contains a version of Kwant with conservation laws implemented. This notebook contains a simple example to illustrate how to work with conservation laws and the scattering matrix.
I invite you and anyone else who is interested to give it a try. We'd appreciate any feedback!
In your case specifically, there would be two projectors in the new implementation - P0 which projects out the spin up block, and P1 that projects out the spin down block. If they are specified in this order, then the spin up and down blocks in the Hamiltonian have block indices 0 and 1, respectively. In the new implementation, it is possible to ask for subblocks of the scattering matrix relating not only any two leads, but also any two conservation law blocks in any leads. To get the reflection amplitude of an incident spin up electron from lead 0 into an outgoing spin down electron in lead 0, you could simply do smat.submatrix((0, 1), (0, 0)). Here, the arguments are tuples of indices (lead index, block index).
Best regards, Tómas
On Fri, Jan 6, 2017 at 3:46 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Hi again,
This question is basically the same as this: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg0007 6 .html
I want to calculate some things using the scattering matrix. I started out with a very simple system, most basic two-terminal system. For some energy there is one propagating mode. I now add matrix structure to the mix (just multiply by s_0 everywhere) and there are now 2 propagating modes (which makes sense).
Now, if I look at the reflection coefficients for lead 0 by using submatrix(0,0), it is now a 2x2 matrix after I introduced the matrices. How are the elements ordered? Is it
[[r_upup, r_updown],[r_downup, r_downdown]]
I know that I could make two lattices, but since I do not plan to use the other functions such as transmission. I just want the smatrix.
Hope you can help me, and thanks in advance.
Best regards,
Camilla
Hi Anton,
Thank you! It is working now. I have one question though, about the conservation laws and Kwant.
So, I tried to add a really small zeeman-field in the leads (delta_z * sigma_z) sot that the two spin states are not degenerate. The idea was that it would be small enough to not affect the physics, but still force the spin-basis. However when I compare the smatrix.submatrix(1,0) in the case where I add the small Zeeman field, and the one I get using the conservation laws, they are not the same.
Do you have any idea as to why?
Also, what is the convention in the numbering of the spins (q_0 and q_1)? Is q_0 = q_1 = 0 upup? It seems that the syntax has changed since you used set_symmetry before?
Best, Camilla ________________________________________ Fra: Anton Akhmerov anton.akhmerov@gmail.com Sendt: 14. februar 2017 09:48 Til: Camilla Espedal Kopi: kwant-discuss@kwant-project.org Emne: Re: [Kwant] Regarding smatrix and spin
Hi Camilla,
Sure. You need to install a development version of tinyarray. If you got everything via conda, then you can do " conda install -c kwant 'tinyarray==dev' ". If you installed kwant via pip, do " pip install git+https://gitlab.kwant-project.org/kwant/tinyarray.git@master "
Let me know if it works (both the installation and using the conservation laws).
Best, Anton
On Tue, Feb 14, 2017 at 9:40 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
sorry for troubling you again.
so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
Best,
Camilla
The code if needed:
import kwant import tinyarray as ta import numpy as np from scipy import sparse from matplotlib import pyplot import matplotlib
s0 = ta.array([[1, 0], [0, 1]]) sx = ta.array([[0, 1], [1, 0]]) sy = ta.array([[0, 1j], [-1j, 0]]) sz = ta.array([[1, 0], [0, -1]])
# Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2
def make_system(t=1.0, W=10, L=10): # Now we must specify the number of orbitals per site. lat = kwant.lattice.square(norbs=2) syst = kwant.Builder()
syst[(lat(x, y) for x in range(L) for y in range(W))] = \ lambda s, alpha, E_z: 4 * t * s0 + E_z * sz syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx # The new bit: specifying the conservation law. lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law=-sz, time_reversal=s0) lead[(lat(0, j) for j in range(W))] = 4 * t * s0 lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead. syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst
syst = make_system(t=1.0, W=10, L=10) energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in energies]
fig = pyplot.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1)
# Like previously smatrix.transmission(lead1, lead0) is transmission from lead0 to lead1 ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices], label='total')
# The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the transmission from the # q0 block of the lead0 into the q1 block of lead1. The subblock ordering is same as we used # in set_symmetry. ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in smatrices], label='$G_{↑↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in smatrices], label='$G_{↑↓}$') ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in smatrices], label='$G_{↓↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in smatrices], label='$G_{↓↓}$') ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large');
On 24. jan. 2017 13:18, Anton Akhmerov wrote:
OK, please double-check the remaining simulation parameters.
Anton
On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
I triend changing it, but that does not solve the problem.
Best,
Camilla
From: Anton Akhmerov [mailto:anton.akhmerov+kd@gmail.com] Sent: 24. januar 2017 12:36
To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
Could the difference originate from you using a lattice constant of 2 instead of 1?
Anton
On Tue, Jan 24, 2017, 10:41 Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
Thanks again for all your help. I will try to do it the linux way. Just one more thing regarding this. I wrote a script in the old Kwant to find the total conductance and compare it to the one in your notebook. While the two plots are qualitatively similar, they are not the same. Am I missing something, or am I calculating different things?
Best, Camilla
(my code):
# Tutorial 2.3.1. Matrix structure of on-site and hopping elements # ================================================================ # # Physics background # ------------------ # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng, # as theoretically predicted in # http://prl.aps.org/abstract/PRL/v90/i25/e256601 # and (supposedly) experimentally oberved in # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html # # Kwant features highlighted # -------------------------- # - Numpy matrices as values in Builder
import kwant
# For plotting import matplotlib.pyplot as plt
# For matrix support import tinyarray import numpy as np
# define Pauli-matrices for convenience sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, 1j], [-1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])
def make_system(a=2, t=1.0, alpha=0.1, e_z=0.05, W=10, L=10): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity). lat = kwant.lattice.square(a)
sys = kwant.Builder() #### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 # hoppings in x-direction lead[lat.neighbors()] = \ -t * sigma_0 #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys
def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(1, 0))
pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show()
def main(): sys = make_system()
# Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(sys, energy) for energy in energies] fig = plt.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1) ax.plot(energies, [smatrix.transmission(1,0) for smatrix in smatrices],
label='total')
ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large') plt.show()
# Call the main function if the script gets executed (as opposed to imported). # See http://docs.python.org/library/__main__.html. if __name__ == '__main__': main()
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 17. januar 2017 10:48 To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
It seems that you are trying to install Kwant on windows. This is a very hard task, and I fear none of the Kwant developers has enough knowledge of it right now (our Windows packages are built by Christoph Gohlke, see [1] for the build environment description). However if you are using windows 10, I suggest to try to install Kwant using the windows subsystem for linux. That way the standard Ubuntu build procedure should work for you.
Best, Anton
On Mon, Jan 16, 2017 at 9:45 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Thanks a lot. I tried to install the cons_laws_combined, but I get the following error message:
"LINK: fatal error LNK1181: cannot open input file 'lapack.lib'"
Is there some package or installation I am missing?
Best regards, Camilla
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 8. januar 2017 16:35 To: Tómas Örn Rosdahl torosdahl@gmail.com Cc: Camilla Espedal camilla.espedal@ntnu.no; kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Hi Camilla, everyone,
I've slightly modified Tómas's example to a case where the spins do get coupled, check it out: http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductanc e.ipynb
I've also provided more detailed installation instructions in the notebook.
Cheers, Anton
On Sun, Jan 8, 2017 at 2:45 PM, Tómas Örn Rosdahl torosdahl@gmail.com wrote:
Dear Camilla,
For a Hamiltonian with degeneracies due to a conservation law, the scattering states will in general not have a definite value of the conservation law. In your case, Kwant returns scattering states that are arbitrary linear combinations of spin up and down, so it is not possible to label the amplitudes in the scattering matrix by spin.
However, in Kwant 1.3 a feature will be added that allows for the construction of scattering states with definite values of a conservation law. See here for an explanation of the basic idea behind the algorithm.
We're currently working on implementing this feature in Kwant itself. The good news is that we're practically done - here is a link to a git repo with a functioning implementation. After you clone the repo, check out the branch cons_laws_combined, which contains a version of Kwant with conservation laws implemented. This notebook contains a simple example to illustrate how to work with conservation laws and the scattering matrix.
I invite you and anyone else who is interested to give it a try. We'd appreciate any feedback!
In your case specifically, there would be two projectors in the new implementation - P0 which projects out the spin up block, and P1 that projects out the spin down block. If they are specified in this order, then the spin up and down blocks in the Hamiltonian have block indices 0 and 1, respectively. In the new implementation, it is possible to ask for subblocks of the scattering matrix relating not only any two leads, but also any two conservation law blocks in any leads. To get the reflection amplitude of an incident spin up electron from lead 0 into an outgoing spin down electron in lead 0, you could simply do smat.submatrix((0, 1), (0, 0)). Here, the arguments are tuples of indices (lead index, block index).
Best regards, Tómas
On Fri, Jan 6, 2017 at 3:46 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Hi again,
This question is basically the same as this: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg0007 6 .html
I want to calculate some things using the scattering matrix. I started out with a very simple system, most basic two-terminal system. For some energy there is one propagating mode. I now add matrix structure to the mix (just multiply by s_0 everywhere) and there are now 2 propagating modes (which makes sense).
Now, if I look at the reflection coefficients for lead 0 by using submatrix(0,0), it is now a 2x2 matrix after I introduced the matrices. How are the elements ordered? Is it
[[r_upup, r_updown],[r_downup, r_downdown]]
I know that I could make two lattices, but since I do not plan to use the other functions such as transmission. I just want the smatrix.
Hope you can help me, and thanks in advance.
Best regards,
Camilla
Hi Camilla,
The reason you are seeing different scattering matrices is because without knowledge of the conservation laws Kwant orders the modes by their velocities first, and not by their internal degrees of freedom. Transmissions should be the same, however.
The updated way to specify the conservation laws is much simpler than in the first draft implementation that we shared. You just need to provide the conserved quantity on each site when constructing the system (e.g. s_z). This operator must have integer eigenvalues. Then the blocks correspond to the eigenvalues of that operator sorted in ascending order (so (0, 1) comes first, (1, 0) second).
Best, Anton
On Tue, Feb 14, 2017 at 11:26 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Hi Anton,
Thank you! It is working now. I have one question though, about the conservation laws and Kwant.
So, I tried to add a really small zeeman-field in the leads (delta_z * sigma_z) sot that the two spin states are not degenerate. The idea was that it would be small enough to not affect the physics, but still force the spin-basis. However when I compare the smatrix.submatrix(1,0) in the case where I add the small Zeeman field, and the one I get using the conservation laws, they are not the same.
Do you have any idea as to why?
Also, what is the convention in the numbering of the spins (q_0 and q_1)? Is q_0 = q_1 = 0 upup? It seems that the syntax has changed since you used set_symmetry before?
Best, Camilla ________________________________________ Fra: Anton Akhmerov anton.akhmerov@gmail.com Sendt: 14. februar 2017 09:48 Til: Camilla Espedal Kopi: kwant-discuss@kwant-project.org Emne: Re: [Kwant] Regarding smatrix and spin
Hi Camilla,
Sure. You need to install a development version of tinyarray. If you got everything via conda, then you can do " conda install -c kwant 'tinyarray==dev' ". If you installed kwant via pip, do " pip install git+https://gitlab.kwant-project.org/kwant/tinyarray.git@master "
Let me know if it works (both the installation and using the conservation laws).
Best, Anton
On Tue, Feb 14, 2017 at 9:40 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
sorry for troubling you again.
so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
Best,
Camilla
The code if needed:
import kwant import tinyarray as ta import numpy as np from scipy import sparse from matplotlib import pyplot import matplotlib
s0 = ta.array([[1, 0], [0, 1]]) sx = ta.array([[0, 1], [1, 0]]) sy = ta.array([[0, 1j], [-1j, 0]]) sz = ta.array([[1, 0], [0, -1]])
# Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2
def make_system(t=1.0, W=10, L=10): # Now we must specify the number of orbitals per site. lat = kwant.lattice.square(norbs=2) syst = kwant.Builder()
syst[(lat(x, y) for x in range(L) for y in range(W))] = \ lambda s, alpha, E_z: 4 * t * s0 + E_z * sz syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx # The new bit: specifying the conservation law. lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law=-sz, time_reversal=s0) lead[(lat(0, j) for j in range(W))] = 4 * t * s0 lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead. syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst
syst = make_system(t=1.0, W=10, L=10) energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in energies]
fig = pyplot.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1)
# Like previously smatrix.transmission(lead1, lead0) is transmission from lead0 to lead1 ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices], label='total')
# The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the transmission from the # q0 block of the lead0 into the q1 block of lead1. The subblock ordering is same as we used # in set_symmetry. ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in smatrices], label='$G_{↑↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in smatrices], label='$G_{↑↓}$') ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in smatrices], label='$G_{↓↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in smatrices], label='$G_{↓↓}$') ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large');
On 24. jan. 2017 13:18, Anton Akhmerov wrote:
OK, please double-check the remaining simulation parameters.
Anton
On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
I triend changing it, but that does not solve the problem.
Best,
Camilla
From: Anton Akhmerov [mailto:anton.akhmerov+kd@gmail.com] Sent: 24. januar 2017 12:36
To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
Could the difference originate from you using a lattice constant of 2 instead of 1?
Anton
On Tue, Jan 24, 2017, 10:41 Camilla Espedal camilla.espedal@ntnu.no wrote:
Dear Anton,
Thanks again for all your help. I will try to do it the linux way. Just one more thing regarding this. I wrote a script in the old Kwant to find the total conductance and compare it to the one in your notebook. While the two plots are qualitatively similar, they are not the same. Am I missing something, or am I calculating different things?
Best, Camilla
(my code):
# Tutorial 2.3.1. Matrix structure of on-site and hopping elements # ================================================================ # # Physics background # ------------------ # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng, # as theoretically predicted in # http://prl.aps.org/abstract/PRL/v90/i25/e256601 # and (supposedly) experimentally oberved in # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html # # Kwant features highlighted # -------------------------- # - Numpy matrices as values in Builder
import kwant
# For plotting import matplotlib.pyplot as plt
# For matrix support import tinyarray import numpy as np
# define Pauli-matrices for convenience sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, 1j], [-1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]])
def make_system(a=2, t=1.0, alpha=0.1, e_z=0.05, W=10, L=10): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity). lat = kwant.lattice.square(a)
sys = kwant.Builder() #### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 # hoppings in x-direction lead[lat.neighbors()] = \ -t * sigma_0 #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys
def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(1, 0))
pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show()
def main(): sys = make_system()
# Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(sys, energy) for energy in energies] fig = plt.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1) ax.plot(energies, [smatrix.transmission(1,0) for smatrix in smatrices],
label='total')
ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large') plt.show()
# Call the main function if the script gets executed (as opposed to imported). # See http://docs.python.org/library/__main__.html. if __name__ == '__main__': main()
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 17. januar 2017 10:48 To: Camilla Espedal camilla.espedal@ntnu.no Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Dear Camilla,
It seems that you are trying to install Kwant on windows. This is a very hard task, and I fear none of the Kwant developers has enough knowledge of it right now (our Windows packages are built by Christoph Gohlke, see [1] for the build environment description). However if you are using windows 10, I suggest to try to install Kwant using the windows subsystem for linux. That way the standard Ubuntu build procedure should work for you.
Best, Anton
On Mon, Jan 16, 2017 at 9:45 AM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Thanks a lot. I tried to install the cons_laws_combined, but I get the following error message:
"LINK: fatal error LNK1181: cannot open input file 'lapack.lib'"
Is there some package or installation I am missing?
Best regards, Camilla
-----Original Message----- From: anton.akhmerov@gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 8. januar 2017 16:35 To: Tómas Örn Rosdahl torosdahl@gmail.com Cc: Camilla Espedal camilla.espedal@ntnu.no; kwant-discuss@kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin
Hi Camilla, everyone,
I've slightly modified Tómas's example to a case where the spins do get coupled, check it out: http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductanc e.ipynb
I've also provided more detailed installation instructions in the notebook.
Cheers, Anton
On Sun, Jan 8, 2017 at 2:45 PM, Tómas Örn Rosdahl torosdahl@gmail.com wrote:
Dear Camilla,
For a Hamiltonian with degeneracies due to a conservation law, the scattering states will in general not have a definite value of the conservation law. In your case, Kwant returns scattering states that are arbitrary linear combinations of spin up and down, so it is not possible to label the amplitudes in the scattering matrix by spin.
However, in Kwant 1.3 a feature will be added that allows for the construction of scattering states with definite values of a conservation law. See here for an explanation of the basic idea behind the algorithm.
We're currently working on implementing this feature in Kwant itself. The good news is that we're practically done - here is a link to a git repo with a functioning implementation. After you clone the repo, check out the branch cons_laws_combined, which contains a version of Kwant with conservation laws implemented. This notebook contains a simple example to illustrate how to work with conservation laws and the scattering matrix.
I invite you and anyone else who is interested to give it a try. We'd appreciate any feedback!
In your case specifically, there would be two projectors in the new implementation - P0 which projects out the spin up block, and P1 that projects out the spin down block. If they are specified in this order, then the spin up and down blocks in the Hamiltonian have block indices 0 and 1, respectively. In the new implementation, it is possible to ask for subblocks of the scattering matrix relating not only any two leads, but also any two conservation law blocks in any leads. To get the reflection amplitude of an incident spin up electron from lead 0 into an outgoing spin down electron in lead 0, you could simply do smat.submatrix((0, 1), (0, 0)). Here, the arguments are tuples of indices (lead index, block index).
Best regards, Tómas
On Fri, Jan 6, 2017 at 3:46 PM, Camilla Espedal camilla.espedal@ntnu.no wrote:
Hi again,
This question is basically the same as this: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg0007 6 .html
I want to calculate some things using the scattering matrix. I started out with a very simple system, most basic two-terminal system. For some energy there is one propagating mode. I now add matrix structure to the mix (just multiply by s_0 everywhere) and there are now 2 propagating modes (which makes sense).
Now, if I look at the reflection coefficients for lead 0 by using submatrix(0,0), it is now a 2x2 matrix after I introduced the matrices. How are the elements ordered? Is it
[[r_upup, r_updown],[r_downup, r_downdown]]
I know that I could make two lattices, but since I do not plan to use the other functions such as transmission. I just want the smatrix.
Hope you can help me, and thanks in advance.
Best regards,
Camilla
Hi,
so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message:
File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int()
Do you know what the problem could be?
It appears that you are using the bleeding-edge version of kwant. You also need the bleeding-edge version of tinyarray as well.
If you are using "conda" to install everything you can just say
conda install -c kwant tinyarray
to install bleeding-edge tinyarray from the kwant channel, or if you are using "pip" you can say
pip install git+https://gitlab.kwant-project.org/kwant/tinyarray
Joe