Kwant-discuss September 2015

kwant-discuss@python.org

22 participants
32 discussions

by ZHANG Bing

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

4 months, 1 week

New instructions for Windows installation

by Michael Wimmer

Dear kwant users, we have posted new instructions for installing kwant on Windows on the kwant website: http://www.kwant-project.org/install The old instructions do not work any more, as the format of the python packages on Christoph Gohlke's webpage have changed. Best regards, the kwant team

6 years

QZ Iteration fails

by Maximilian Trescher

Dear kwant users and developers, this is my first post to this list, I'm a PhD student from Berlin. Currently I'm trying to implement a lattice model of a pyrochlore slab in kwant. I found a (more or less straightforward) way to introduce periodic boundary conditions in the system in the maillinglist archive. This works very nicely as long as I keep the periodicity along a lattice vector. But I run into problems when I choose different directions: Most of the time all solvers fail with a "LinAlgError: QZ iteration failed to converge in zgges". I know about this post http://comments.gmane.org/gmane.comp.science.kwant.user/372 but in my case it occurs not only for a band bottom, but for a range of energies. To give you all the details I prepared a Ipython notebook that you can view here: http://nbviewer.ipython.org/gist/faucon/729050da5e3f2eae1bb8# (Note that the inclusion of complex next-nearest-neighbor hopping is crucial to produce the error, I tried to create the shortest example which reproduces my problem). Do you have any idea how to circumvent this problem? Is it somehow related to http://netlib.org/lapack/Errata/vrac/lapack_known_issues.html#QZ this problem in Lapack? I would be thankful for any hint, Best, Maximilian

6 years, 2 months

ldos.cumsum or ldos.cumprod

by Dedi Setiabudidaya

Hi there, I tried the functions ldos.cunsum() and ldos.cumprod() and succeeded in obtaining the plot;but I do not know what the plots told me. Anyone can help ?Below is the codes for the plot data1 = []energies = np.linspace(1,4,101)for energy in energies: ldos = kwant.ldos(sys,energy) data1.append(ldos.cumsum())pyplot.figure()pyplot.plot(energies, data1)pyplot.xlabel("energy [t]")pyplot.ylabel("ldos")pyplot.show() and for the other plot I just changed the function ldos.cumsum() with ldos.cumprod(). Thank you in advance. Kind Regards, Dedi

6 years, 3 months

Scotch/MUMPS from source vs from repositories

by Baris Pekerten

Dear all, Is there a significant speed difference between MUMPS/scotch from Ubuntu repos vs. from source, especially considering that Kwant uses only the single core algorithms? Latest MUMPS in the Ubuntu repos is 4.10. Latest stable release of MUMPS is 5.0.5. I try to install everything from source. Speed is an issue for me. (Last work I did involved ~2M runs of a 4x4 hamiltonian defined on a 4x60000 wire with random potential per plot, which took ~16 days per plot with the computational power available to me.) However, it's easy (for me) to have a MUMPS installation go wrong, so I'd rather install them from repos unless there's a significant speed advantage. Thank you for your time and concern, Baris

6 years, 3 months

kkghosh

by kamal ghosh

Dear all, Please help me in correcting the following program which I tried to mimic a portion of the program on transmission through a quantum well. I tried the following: import kwant import cmath lat=kwant.lattice.square(1) sys=kwant.Builder() def potential(site,pot): (x,y)=site.pos if 10 < x< 20: return pot else: return 0 def onsite(site,pot=0): return potential(site,pot) print potential(12,0) Error shown : (x,y)=site.pos; there is no attribute in int (x,y)= site.pos It is strange that in the original program of the quantum well, I also could not explain why that program run successfully! because there also no such "pos" attribute is defined anywhere. Please bear with my misunderstanding and rectify me with brief tutorial. K.K.Ghosh mail: kk_ghosh(a)rediffmail.com

6 years, 3 months

Dynamic number of lattices

by Baris Pekerten

Dear all, I need to calculate a system with a variable number of 2D lattices. So, the pseudo code should look like: for i in xrange(2,100): # Form a system with (i) number of lattices, with hoppings that depend on (i) in between the lattices # Calculate stuff, such as the transmission amplitude from lead f of lattice j to lead g of lattice k (j, k <= i) # plot calculated stuff as a function of i I couldn't figure out a straight method to do it, as I have to pass (i) as a function variable when I'm forming the hoppings. That is, in the make_system part of the code, I need to say things like (again in pseudo code) syst[(lat(i, x, y), lat(i+1, x, y) for x in ... for y in ...)] = hopping(i, i+1) which is impossible because a) lattice definitions can only take in realspace coordinates and b) the function on the right side has to have two sites as its first two arguments and the rest will be provided in the solver part of the code. I found two rather inelegant possible solutions to my problem. (I'm trying only the second one). What I'm asking is, is there a better solution? Inelegant (and possibly wrong) solution 1: Make this a truly 3D rectangular prism system, with each layer corresponding to one lattice. This makes the problem of writing the hoppings trivial, but then how would I get the transmission amplitude from the left lead of 2D lattice number 35 to the right lead of 2D lattice number 67? Inelegant solution 2: Code-generating code. This is what I've done. Essentially, I generate a .py file with 100 copies of the make_system function, each with different number of lattices. Later, in the main code, I import the appropriate make_system function from this .py file and solve my system. Thank you all for your time and concern. Cheers, Baris P.

6 years, 3 months

Re: [Kwant] Problem with elements of S-matrix not being smooth

by Anton Akhmerov

Hi Simon, > This helps a lot!! I think it may also help others to mention this in the > tutorial somewhere if it doesn't already. (Apologies, I may have missed it). Good idea, do you have a specific place in mind where this remark could go? You're welcome to submit corrections to the documentation. Also if you find a good recipe for uniquely fixing the phase, please share it on the mailing list. Best, Anton PS Greetings to Henning > Thank you and best wishes, > > Simon > > On Mon, Sep 28, 2015 at 6:58 PM, Anton Akhmerov <anton.akhmerov(a)gmail.com> > wrote: >> >> Hi Simon, >> >> Kwant algorithms do not adapt any particular convention in choosing >> the phases of the modes in the leads. That's why the scattering matrix >> at different energies can be discontinuous. You can access the wave >> functions of the modes through the resulting smatrix [1]. You can also >> easily modify the way Kwant calculates modes like we've done in [2]. >> >> Hope that helps, >> Anton >> >> [1]: >> http://kwant-project.org/doc/1.0/reference/generated/kwant.solvers.common.S… >> [2]: http://arxiv.org/abs/1408.1563 specifically >> http://arxiv.org/src/1408.1563v2/anc/trijunction.py >> >> >> On Mon, Sep 28, 2015 at 7:41 PM, Simon Malzard <smalzard01(a)gmail.com> >> wrote: >> > Hello Kwant, >> > >> > The problem I am trying to solve relies on being able to calculate the >> > eigenphases of the scattering matrix for different energies, more >> > precisely >> > it requires the elements of the scattering matrix to be smooth as a >> > function >> > of energy. >> > >> > By examining the elements of the scattering matrix as a function of >> > energy, >> > I have noticed that the elements of the scattering matrix are not smooth >> > and >> > there exists a sign problem. >> > >> > The code I have included below is for a highly(!!) simplified example, >> > where >> > the scattering region is simply two leads attached to a single square. I >> > took the base code from the kwant tutorial page to reduce any possible >> > errors. I have taken a small range of energies and plotted the real >> > parts of >> > the off diagonal elements of the scattering matrix. You will notice that >> > plot included demonstrates that the elements of the scattering matrix >> > are >> > not smooth and a sign change occurs for certain energies (sign changes >> > for >> > both the real and imaginary parts, plotting chosen for simplicity). >> > >> > Note that for the example I take a tiny range of energies, where the >> > conductance is the same and hence the number of active modes is constant >> > as >> > a function of energy. >> > >> > There may be a mistake in understanding on my part, however, I believe >> > this >> > error is due to some sign error in the incoming or outgoing states in >> > the >> > lead as this only effects individual modes (as you will see when you >> > adjust >> > the system size, or move up to the next conductance plateau and the size >> > of >> > the scattering matrix increases. My initial program was looking at >> > graphene >> > for a large rectangular flake and I noticed this effect considerably). I >> > think this is a boundedness problem for certain functions which >> > describes >> > the individual scattering states at certain energies. >> > >> > Is this intentional behaviour for KWANT? As it means I can't perform >> > calculations such as calculating the Wigner-Smith time-delay matrix, >> > among >> > other scattering characteristics. >> > >> > Thank you for your time + best wishes, >> > >> > Simon >> > >> > >> > My code: >> > >> > >> > #### KWANT tutorial code >> > from matplotlib import pyplot as plt >> > import kwant >> > import numpy as np >> > import scipy.linalg as la >> > # First, define the tight-binding system >> > >> > sys = kwant.Builder() >> > >> > # Here, we are only working with square lattices >> > a = 1 >> > lat = kwant.lattice.square(a) >> > >> > t = 1.0 >> > W = 2 >> > L = 2 >> > >> > # Define the scattering region >> > >> > for i in xrange(L): >> > for j in xrange(W): >> > # On-site Hamiltonian >> > sys[lat(i, j)] = 4 * t >> > >> > # Hopping in y-direction >> > if j > 0: >> > sys[lat(i, j), lat(i, j - 1)] = -t >> > >> > # Hopping in x-direction >> > if i > 0: >> > sys[lat(i, j), lat(i - 1, j)] = -t >> > >> > # Then, define and attach the leads: >> > >> > # First the lead to the left >> > # (Note: TranslationalSymmetry takes a real-space vector) >> > sym_left_lead = kwant.TranslationalSymmetry((-a, 0)) >> > left_lead = kwant.Builder(sym_left_lead) >> > >> > for j in xrange(W): >> > left_lead[lat(0, j)] = 4 * t >> > if j > 0: >> > left_lead[lat(0, j), lat(0, j - 1)] = -t >> > left_lead[lat(1, j), lat(0, j)] = -t >> > >> > sys.attach_lead(left_lead) >> > >> > # Then the lead to the right >> > sym_right_lead = kwant.TranslationalSymmetry((a, 0)) >> > right_lead = kwant.Builder(sym_right_lead) >> > >> > for j in xrange(W): >> > right_lead[lat(0, j)] = 4 * t >> > if j > 0: >> > right_lead[lat(0, j), lat(0, j - 1)] = -t >> > right_lead[lat(1, j), lat(0, j)] = -t >> > >> > sys.attach_lead(right_lead) >> > >> > # Plot it, to make sure it's OK >> > kwant.plot(sys) >> > >> > # Finalize the system >> > sys = sys.finalized() >> > >> > # Now that we have the system, we can compute conductance >> > >> > emin, emax = 1.05, 1.06#3.00 >> > points = 21 >> > >> > energies = np.linspace(emin,emax,points) >> > element_0_1, element_1_0 = [], [] >> > >> > for ie in energies: >> > >> > energy = ie >> > # I only consider element 0,1 and 1,0 as 0,0 and 1,1 are vanishingly >> > small and look like floating point errors. >> > >> > #This gets the smartix and looks at the real parts of the >> > off-diagonal >> > elements >> > smatrix = kwant.smatrix(sys, energy).data >> > element_0_1.append(smatrix[0,1].real) >> > element_1_0.append(smatrix[1,0].real) >> > >> > print smatrix[0,1].real >> > print smartix[1,0].real >> > >> > fig2 = plt.figure() >> > ax2 = fig2.add_subplot(1,1,1) >> > ax2.plot(element_0_1, 'ro') >> > ax2.plot(element_1_0, 'bo') >> > plt.show() >> > > >

6 years, 3 months

Re: [Kwant] Site ordering while plotting wavefunction

by Anton Akhmerov

> I was wondering if there is some link which explains how to put hoppings for > a 3D system. The general procedure: sys[lat(i, j, k), lat(i - 1, j, k)] = > -t doesn't seem to work and gives an error: Polyatomic object not callable. You seem to be using a lattice with more than one sublattice, check out the graphene tutorial (kwant-project.org/doc/1.0/tutorial/tutorial4.html). Otherwise 3D isn't different from 2D. Best, Anton > Thank you and regards, > Girish > > On Sun, Sep 27, 2015 at 8:53 AM, Anton Akhmerov <anton.akhmerov(a)gmail.com> > wrote: >> >> Dear Girish, >> >> See the example of plotting an 1D wave function over here: >> >> http://nbviewer.ipython.org/github/topocm/topocm_content/blob/master/w1_top… >> >> Best, >> Anton >> >> On Fri, Sep 25, 2015 at 9:16 PM, Girish Sharma <girishs(a)g.clemson.edu> >> wrote: >> > Hi, >> > >> > I have attached a small code, trying to visualize Majorana wavefunctions >> > at >> > the two end points of my 1D wire. The kwant.plotter doesn't really help, >> > so >> > I'm trying basic pyplot. However, due to random ordering of sites, I do >> > not >> > see the wavefunction peaking at the ends (see the last plot). Is there a >> > way >> > out to do this ordering correctly in PYTHON? >> > >> > Thank you for your time ! >> > >> > Best regards, >> > Girish > >

6 years, 3 months

Problem with elements of S-matrix not being smooth

by Simon Malzard

Hello Kwant, The problem I am trying to solve relies on being able to calculate the eigenphases of the scattering matrix for different energies, more precisely it requires the elements of the scattering matrix to be smooth as a function of energy. By examining the elements of the scattering matrix as a function of energy, I have noticed that the elements of the scattering matrix are not smooth and there exists a sign problem. The code I have included below is for a highly(!!) simplified example, where the scattering region is simply two leads attached to a single square. I took the base code from the kwant tutorial page to reduce any possible errors. I have taken a small range of energies and plotted the real parts of the off diagonal elements of the scattering matrix. You will notice that plot included demonstrates that the elements of the scattering matrix are not smooth and a sign change occurs for certain energies (sign changes for both the real and imaginary parts, plotting chosen for simplicity). Note that for the example I take a tiny range of energies, where the conductance is the same and hence the number of active modes is constant as a function of energy. There may be a mistake in understanding on my part, however, I believe this error is due to some sign error in the incoming or outgoing states in the lead as this only effects individual modes (as you will see when you adjust the system size, or move up to the next conductance plateau and the size of the scattering matrix increases. My initial program was looking at graphene for a large rectangular flake and I noticed this effect considerably). I think this is a boundedness problem for certain functions which describes the individual scattering states at certain energies. Is this intentional behaviour for KWANT? As it means I can't perform calculations such as calculating the Wigner-Smith time-delay matrix, among other scattering characteristics. Thank you for your time + best wishes, Simon My code: #### KWANT tutorial code from matplotlib import pyplot as plt import kwant import numpy as np import scipy.linalg as la # First, define the tight-binding system sys = kwant.Builder() # Here, we are only working with square lattices a = 1 lat = kwant.lattice.square(a) t = 1.0 W = 2 L = 2 # Define the scattering region for i in xrange(L): for j in xrange(W): # On-site Hamiltonian sys[lat(i, j)] = 4 * t # Hopping in y-direction if j > 0: sys[lat(i, j), lat(i, j - 1)] = -t # Hopping in x-direction if i > 0: sys[lat(i, j), lat(i - 1, j)] = -t # Then, define and attach the leads: # First the lead to the left # (Note: TranslationalSymmetry takes a real-space vector) sym_left_lead = kwant.TranslationalSymmetry((-a, 0)) left_lead = kwant.Builder(sym_left_lead) for j in xrange(W): left_lead[lat(0, j)] = 4 * t if j > 0: left_lead[lat(0, j), lat(0, j - 1)] = -t left_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(left_lead) # Then the lead to the right sym_right_lead = kwant.TranslationalSymmetry((a, 0)) right_lead = kwant.Builder(sym_right_lead) for j in xrange(W): right_lead[lat(0, j)] = 4 * t if j > 0: right_lead[lat(0, j), lat(0, j - 1)] = -t right_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(right_lead) # Plot it, to make sure it's OK kwant.plot(sys) # Finalize the system sys = sys.finalized() # Now that we have the system, we can compute conductance emin, emax = 1.05, 1.06#3.00 points = 21 energies = np.linspace(emin,emax,points) element_0_1, element_1_0 = [], [] for ie in energies: energy = ie # I only consider element 0,1 and 1,0 as 0,0 and 1,1 are vanishingly small and look like floating point errors. #This gets the smartix and looks at the real parts of the off-diagonal elements smatrix = kwant.smatrix(sys, energy).data element_0_1.append(smatrix[0,1].real) element_1_0.append(smatrix[1,0].real) print smatrix[0,1].real print smartix[1,0].real fig2 = plt.figure() ax2 = fig2.add_subplot(1,1,1) ax2.plot(element_0_1, 'ro') ax2.plot(element_1_0, 'bo') plt.show()

6 years, 3 months

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Kwant-discuss September 2015