Dear sir, I have updated KWANT, but it shows the *AttributeError: module 'kwant.continuum' has no attribute 'discretize_landau'.* And in browser also, it is showing the same error. I have downloaded the landau_levels.py file and put it into the continuum folder. But it is not working.
On Wed, Sep 11, 2019, 23:47 Naveen Yadav <naveengunwa...@gmail.com> wrote: > Dear sir, > > That is exactly what I am looking for. > But in my case Hamiltonian is not polynomial in k. It contains Sine and > Cosine terms. It's a tight binding Hamiltonian having coupling terms like > sigma_x *Sin(kx)+ sigma_y *sin(ky) and mass term in the trignometric form. > So, can I proceed by writing the trignometric terms in some lower order > polynomial terms? Does that make sense? > Please make some comment regarding this. > Thank you very much. > > > > > > > > > > Naveen > Department of Physics & Astrophysics > University of Delhi > New Delhi-110007 > > On Wed, Sep 11, 2019, 22:18 Anton Akhmerov <anton.akhmerov...@gmail.com> > wrote: > >> Dear Naveen, >> >> If you are dealing with a continuum Hamiltonian (so a polynomial in >> k-space), then there is a recent addition to Kwant, that allows to >> compute Landau levels. Please check out if this tutorial is what you >> are looking for: >> >> https://kwant-project.org/doc/dev/tutorial/magnetic_field#adding-magnetic-field >> (if you click the "activate thebelab" button, you can also play around >> with the code in your browser). >> >> If that suits your needs, you'd need to either install a development >> version of Kwant or just get this file: >> >> https://gitlab.kwant-project.org/kwant/kwant/blob/master/kwant/continuum/landau_levels.py >> >> Let me know if that answers your question, >> Anton >> >> On Wed, 11 Sep 2019 at 18:39, Naveen Yadav <naveengunwa...@gmail.com> >> wrote: >> > >> > Dear sir, >> > >> > I understood that this code is off no use. The leads are useless here. >> > Actually, I want to plot the Landau fan. Can KWANT do the job here? >> > >> > >> > >> > >> > >> > >> > >> > >> > >> > >> > >> > Naveen >> > Department of Physics & Astrophysics >> > University of Delhi >> > New Delhi-110007 >> > >> > On Mon, Sep 9, 2019, 00:50 Abbout Adel <abbout.a...@gmail.com> wrote: >> >> >> >> Dear Naveen, >> >> >> >> If your concern is the program which is slow, that is not an issue >> since it takes just few minutes. >> >> Now, if you are talking about the result, I want to be sure that you >> notice that your system is not infinite as you claim in your email. >> >> You can check that by adding extra cells from the lead" >> syst.attach_lead(lead, add_cells=10) >> >> Actually, in your case, the presence of the leads is useless since at >> the end, you are just diagonalizing the Hamiltonian of the central system. >> >> If you want to study an infinite system in x and y, you need to look >> at the module "wraparound" and the example of graphene that is in the >> archive of kwant. >> >> For the magnetic field, you can use the Pierls substitution. check for >> example this paper [1] >> >> >> >> You can also think about the use of continuous Hamiltonian in kwant. >> You may find it very useful [2] >> >> I hope this helps. >> >> >> >> Regards, >> >> Adel >> >> >> >> >> >> [1] https://arxiv.org/pdf/1601.06507.pdf >> >> [2] https://kwant-project.org/doc/1/tutorial/discretize >> >> >> >> On Sun, Sep 8, 2019 at 6:16 PM Naveen Yadav <naveengunwa...@gmail.com> >> wrote: >> >>> >> >>> Dear Sir, >> >>> Thanks for the tips. As you told, I have tried in other way also but >> I am getting the same result which are very tedious. I don't know where is >> fault. >> >>> Now the code looks like >> >>> >> >>> import kwant >> >>> import scipy.sparse.linalg as sla >> >>> import matplotlib.pyplot as plt >> >>> import tinyarray >> >>> import numpy as np >> >>> from numpy import cos, sin, pi >> >>> import cmath >> >>> from cmath import exp >> >>> >> >>> 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=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0, >> t_z=1.0, lamda=0.1, beta=1.05): >> >>> def onsite(site): >> >>> return (t_z * cos(beta) + 2 * t) * sigma_z >> >>> >> >>> def hoppingx(site0, site1): >> >>> return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x) >> >>> >> >>> def hoppingy(site0, site1): >> >>> return -0.5 * t * sigma_z - 0.5 * 1j * t_y * sigma_y >> >>> >> >>> def hoppingz(site0, site1, B): >> >>> y = site1.pos[1] >> >>> return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) * >> exp(2 * pi * 1j * B * a * (y-40)) >> >>> >> >>> >> >>> syst = kwant.Builder() >> >>> lat = kwant.lattice.cubic(a) >> >>> syst[(lat(z, y, x) for z in range(H) for y in range(W) for x in >> range(L))] = onsite >> >>> syst[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>> syst[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>> syst[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>> >> >>> lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0))) >> >>> lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in >> range(L))]=onsite >> >>> lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>> lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>> lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>> >> >>> syst.attach_lead(lead1) >> >>> syst.attach_lead(lead1.reversed()) >> >>> >> >>> lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0))) >> >>> lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in >> range(L))]=onsite >> >>> lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>> lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>> lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>> >> >>> syst.attach_lead(lead2) >> >>> syst.attach_lead(lead2.reversed()) >> >>> syst = syst.finalized() >> >>> return syst >> >>> >> >>> def analyze_system(syst, Bfields): >> >>> syst = make_system() >> >>> kwant.plot(syst) >> >>> energies = [] >> >>> for B in Bfields: >> >>> #print(B) >> >>> ham_mat = syst.hamiltonian_submatrix(params=dict(B=B), >> sparse=True) >> >>> ev, evec = sla.eigsh(ham_mat.tocsc(), k=20, sigma=0) >> >>> energies.append(ev) >> >>> #print (energies) >> >>> >> >>> plt.figure() >> >>> plt.plot(Bfields, energies) >> >>> plt.xlabel("magnetic field [${10^-3 h/e}$]") >> >>> plt.ylabel("energy [t]") >> >>> >> >>> plt.ylim(0, 0.11) >> >>> plt.show() >> >>> def main(): >> >>> syst = make_system() >> >>> analyze_system(syst, [B * 0.00002 for B in range(101)]) >> >>> main() >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> >> >>> Naveen >> >>> Department of Physics & Astrophysics >> >>> University of Delhi >> >>> New Delhi-110007 >> >>> >> >>> On Sun, Sep 8, 2019, 17:37 Abbout Adel <abbout.a...@gmail.com> wrote: >> >>>> >> >>>> Dear Naveen, >> >>>> >> >>>> Your program works fine. You have just a small problem of plotting. >> You can solve that by changing "plt.show" by "plt.show()". >> >>>> >> >>>> Think about putting print (B) inside the loop when you debug your >> program. That will help you for example to see if the program is running >> well, and you can detect what may be wrong. >> >>>> Think also about returning Energies in your function. This way you >> can try potting the result outside the function you called. Don't hesitate >> to put some extra lines in your program to follow the progress when you >> think that there is a problem. >> >>>> >> >>>> >> >>>> I hope this helps. >> >>>> Regards, >> >>>> Adel >> >>>> >> >>>> On Thu, Sep 5, 2019 at 7:32 PM Naveen Yadav < >> naveengunwa...@gmail.com> wrote: >> >>>>> >> >>>>> Dear Sir, >> >>>>> >> >>>>> I am trying to plot the energy as a function of magnetic field for >> a 3D case, but I am getting tedious results. The system is infinite in two >> directions and has some width in the third direction. Please have a look at >> the code attached below. I tried a lot but failed. Is the code correct or I >> am wrong somewhere. >> >>>>> Thank you. >> >>>>> >> >>>>> >> >>>>> import kwant >> >>>>> import scipy.sparse.linalg as sla >> >>>>> import matplotlib.pyplot as plt >> >>>>> import tinyarray >> >>>>> import numpy as np >> >>>>> from numpy import cos, sin, pi >> >>>>> import cmath >> >>>>> from cmath import exp >> >>>>> >> >>>>> 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=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0, >> t_z=1.0, lamda=0.1, beta=1.05): >> >>>>> def onsite(site): >> >>>>> return (t_z * cos(beta) + 2 * t) * sigma_z >> >>>>> >> >>>>> def hoppingx(site0, site1): >> >>>>> return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x) >> >>>>> >> >>>>> def hoppingy(site0, site1): >> >>>>> return -0.5 * t * sigma_z - 0.5 * 1j * t_y * sigma_y >> >>>>> >> >>>>> def hoppingz(site0, site1, B): >> >>>>> y = site1.pos[1] >> >>>>> return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) >> * exp(2 * pi * 1j * B * a * (y-40)) >> >>>>> >> >>>>> >> >>>>> syst = kwant.Builder() >> >>>>> lat = kwant.lattice.cubic(a) >> >>>>> syst[(lat(z, y, x) for z in range(H) for y in range(W) for x in >> range(L))] = onsite >> >>>>> syst[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>>>> syst[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>>>> syst[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>>>> >> >>>>> lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0))) >> >>>>> lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in >> range(L))]=onsite >> >>>>> lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>>>> lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>>>> lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>>>> >> >>>>> syst.attach_lead(lead1) >> >>>>> syst.attach_lead(lead1.reversed()) >> >>>>> >> >>>>> lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0))) >> >>>>> lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in >> range(L))]=onsite >> >>>>> lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz >> >>>>> lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy >> >>>>> lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx >> >>>>> >> >>>>> syst.attach_lead(lead2) >> >>>>> syst.attach_lead(lead2.reversed()) >> >>>>> syst = syst.finalized() >> >>>>> return syst >> >>>>> >> >>>>> def analyze_system(): >> >>>>> syst = make_system() >> >>>>> kwant.plot(syst) >> >>>>> Bfields = np.linspace(0, 0.002, 100) >> >>>>> energies = [] >> >>>>> for B in Bfields: >> >>>>> ham_mat = syst.hamiltonian_submatrix(params=dict(B=B), >> sparse=True) >> >>>>> ev, evec = sla.eigsh(ham_mat.tocsc(), k=20, sigma=0) >> >>>>> energies.append(ev) >> >>>>> #print(energies) >> >>>>> >> >>>>> plt.figure() >> >>>>> plt.plot(Bfields, energies) >> >>>>> plt.xlabel("magnetic field [${10^-3 h/e}$]") >> >>>>> plt.ylabel("energy [t]") >> >>>>> >> >>>>> plt.ylim(0, 0.11) >> >>>>> plt.show >> >>>>> def main(): >> >>>>> syst = make_system() >> >>>>> analyze_system() >> >>>>> main() >> >>>>> >> >>>>> >> >>>>> >> >>>>> >> >>>>> -- >> >>>>> >> >>>>> >> >>>>> With Best Regards >> >>>>> NAVEEN YADAV >> >>>>> Ph.D Research Scholar >> >>>>> Deptt. Of Physics & Astrophysics >> >>>>> University Of Delhi. >> >>>> >> >>>> >> >>>> >> >>>> -- >> >>>> Abbout Adel >> >> >> >> >> >> >> >> -- >> >> Abbout Adel >> >
