Majorana polarization
Dear Kwant users, I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that? Thanks in advance.
Dear Antonio,
In Kwant 1.3 you can compute expectation values of any local operator,
applied to any wave function, as described in this Kwant tutorial:
https://kwant-project.org/doc/1/tutorial/operators
It is also possible that you can compute what you want using the
output of ldos. The ordering of internal degrees of freedom of each
there is the same as in the Hamiltonian you define.
Best,
Anton
On Mon, Oct 30, 2017 at 9:44 PM, Antonio Lucas Rigotti Manesco
Dear Kwant users,
I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that?
Thanks in advance.
Thanks Anton. I was not aware of these functions.
Best,
Em seg, 30 de out de 2017 19:11, Anton Akhmerov
Dear Antonio,
In Kwant 1.3 you can compute expectation values of any local operator, applied to any wave function, as described in this Kwant tutorial: https://kwant-project.org/doc/1/tutorial/operators
It is also possible that you can compute what you want using the output of ldos. The ordering of internal degrees of freedom of each there is the same as in the Hamiltonian you define.
Best, Anton
On Mon, Oct 30, 2017 at 9:44 PM, Antonio Lucas Rigotti Manesco
wrote: Dear Kwant users,
I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that?
Thanks in advance.
Hi,
As Majorana polarization is a vector field, I am trying to plot the values
using quiver by adding the two functions:
def plot_vector_field(sys, Maj_x, Maj_y):
xmin, ymin = min(s.tag for s in sys.sites)
xmax, ymax = max(s.tag for s in sys.sites)
x, y = np.meshgrid(np.arange(xmin, xmax+1), np.arange(ymin, ymax+1))
plt.quiver(x, y, Maj_x, Maj_y)
plt.show()
def majorana_polarization(sys, energy):
wf = kwant.wave_function(sys, energy)
psi = wf(0)
eup, edown, hup, hdown = psi[::2], psi[1::2], psi[3::2], - psi[2::2]
Maj = eup * hup + edown * hdown
print(Maj)
Maj_x = np.real(Maj)
Maj_y = np.imag(Maj)
plot_vector_field(sys, Maj_x, Maj_y)
But since I am dealing with a honeycomb lattice the meshgrid will not work.
How could I generate that using the sys sites?
2017-10-30 19:10 GMT-02:00 Anton Akhmerov
Dear Antonio,
In Kwant 1.3 you can compute expectation values of any local operator, applied to any wave function, as described in this Kwant tutorial: https://kwant-project.org/doc/1/tutorial/operators
It is also possible that you can compute what you want using the output of ldos. The ordering of internal degrees of freedom of each there is the same as in the Hamiltonian you define.
Best, Anton
On Mon, Oct 30, 2017 at 9:44 PM, Antonio Lucas Rigotti Manesco
wrote: Dear Kwant users,
I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that?
Thanks in advance.
-- Antônio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil
Hi Antonio.
I imagine you could evaluate that vector field at the positions of the
lattice sites and then feed it to an interpolation routine.
Best,
Anton
On Tue, Oct 31, 2017 at 12:35 PM, Antonio Lucas Rigotti Manesco
Hi,
As Majorana polarization is a vector field, I am trying to plot the values using quiver by adding the two functions:
def plot_vector_field(sys, Maj_x, Maj_y): xmin, ymin = min(s.tag for s in sys.sites) xmax, ymax = max(s.tag for s in sys.sites) x, y = np.meshgrid(np.arange(xmin, xmax+1), np.arange(ymin, ymax+1))
plt.quiver(x, y, Maj_x, Maj_y) plt.show()
def majorana_polarization(sys, energy): wf = kwant.wave_function(sys, energy) psi = wf(0) eup, edown, hup, hdown = psi[::2], psi[1::2], psi[3::2], - psi[2::2] Maj = eup * hup + edown * hdown print(Maj) Maj_x = np.real(Maj) Maj_y = np.imag(Maj) plot_vector_field(sys, Maj_x, Maj_y)
But since I am dealing with a honeycomb lattice the meshgrid will not work. How could I generate that using the sys sites?
2017-10-30 19:10 GMT-02:00 Anton Akhmerov
: Dear Antonio,
In Kwant 1.3 you can compute expectation values of any local operator, applied to any wave function, as described in this Kwant tutorial: https://kwant-project.org/doc/1/tutorial/operators
It is also possible that you can compute what you want using the output of ldos. The ordering of internal degrees of freedom of each there is the same as in the Hamiltonian you define.
Best, Anton
On Mon, Oct 30, 2017 at 9:44 PM, Antonio Lucas Rigotti Manesco
wrote: Dear Kwant users,
I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that?
Thanks in advance.
-- Antônio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil
Thanks Anton,
I solved the problem using the following procedure. Maybe it is useful for
someone:
def plot_vector_field(sys, Maj_x, Maj_y):
x = np.zeros(len(sys.sites))
y = np.zeros(len(sys.sites))
for s in range(len(sys.sites)):
x[s], y[s] = sys.pos(s)
plt.quiver(x, y , Maj_x, Maj_y, scale = 50)
plt.xlim(-200,300)
plt.ylim(-200,300)
plt.show()
2017-10-31 17:59 GMT-02:00 Anton Akhmerov
Hi Antonio.
I imagine you could evaluate that vector field at the positions of the lattice sites and then feed it to an interpolation routine.
Best, Anton
On Tue, Oct 31, 2017 at 12:35 PM, Antonio Lucas Rigotti Manesco
wrote: Hi,
As Majorana polarization is a vector field, I am trying to plot the values using quiver by adding the two functions:
def plot_vector_field(sys, Maj_x, Maj_y): xmin, ymin = min(s.tag for s in sys.sites) xmax, ymax = max(s.tag for s in sys.sites) x, y = np.meshgrid(np.arange(xmin, xmax+1), np.arange(ymin, ymax+1))
plt.quiver(x, y, Maj_x, Maj_y) plt.show()
def majorana_polarization(sys, energy): wf = kwant.wave_function(sys, energy) psi = wf(0) eup, edown, hup, hdown = psi[::2], psi[1::2], psi[3::2], - psi[2::2] Maj = eup * hup + edown * hdown print(Maj) Maj_x = np.real(Maj) Maj_y = np.imag(Maj) plot_vector_field(sys, Maj_x, Maj_y)
But since I am dealing with a honeycomb lattice the meshgrid will not work. How could I generate that using the sys sites?
2017-10-30 19:10 GMT-02:00 Anton Akhmerov
: Dear Antonio,
In Kwant 1.3 you can compute expectation values of any local operator, applied to any wave function, as described in this Kwant tutorial: https://kwant-project.org/doc/1/tutorial/operators
It is also possible that you can compute what you want using the output of ldos. The ordering of internal degrees of freedom of each there is the same as in the Hamiltonian you define.
Best, Anton
On Mon, Oct 30, 2017 at 9:44 PM, Antonio Lucas Rigotti Manesco
wrote: Dear Kwant users,
I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it
from
kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that?
Thanks in advance.
-- Antônio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil
-- Antônio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil
participants (2)
-
Anton Akhmerov
-
Antonio Lucas Rigotti Manesco