dear sir, I have tried it for 3D BHZ model but it is not working. Does it work for only 2D system.
On Thu, Sep 12, 2019 at 1:54 PM Anton Akhmerov <anton.akhmerov...@gmail.com> wrote: > Great, > > Just to add a concluding remark: Landau fan requires a continuum > approximation of the Hamiltonian. If you start with a tight-binding > Hamiltonian you'd get fractal spectrum and the Hofstadter butterfly > instead. > > Happy Kwanting, > Anton > > On Thu, 12 Sep 2019 at 10:09, Naveen Yadav <naveengunwa...@gmail.com> > wrote: > > > > The second problem is solved. I got the landau fan for BHZ model. > > Thank you for the support. > > > > > > On Thu, Sep 12, 2019, 12:46 Naveen Yadav <naveengunwa...@gmail.com> > wrote: > >> > >> 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 > -- With Best Regards NAVEEN YADAV Ph.D Research Scholar Deptt. Of Physics & Astrophysics University Of Delhi.
