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 particlehole 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://kwantproject.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 <antoniolrm@usp.br> 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 particlehole 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 <anton.akhmerov+kd@gmail.com> escreveu:
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://kwantproject.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 <antoniolrm@usp.br> 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 particlehole 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? 20171030 19:10 GMT02:00 Anton Akhmerov <anton.akhmerov+kd@gmail.com>:
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://kwantproject.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 <antoniolrm@usp.br> 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 particlehole 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 <antoniolrm@usp.br> 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?
20171030 19:10 GMT02:00 Anton Akhmerov <anton.akhmerov+kd@gmail.com>:
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://kwantproject.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 <antoniolrm@usp.br> 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 particlehole 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() 20171031 17:59 GMT02:00 Anton Akhmerov <anton.akhmerov+kd@gmail.com>:
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 <antoniolrm@usp.br> 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?
20171030 19:10 GMT02:00 Anton Akhmerov <anton.akhmerov+kd@gmail.com>:
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://kwantproject.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 <antoniolrm@usp.br> 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 particlehole 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