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 kwantimport scipy.sparse.linalg as slaimport matplotlib.pyplot as >> pltimport tinyarrayimport numpy as npfrom numpy import cos, sin, piimport >> cmathfrom cmath import expsigma_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 systdef 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 kwantimport scipy.sparse.linalg as slaimport matplotlib.pyplot >>>> as pltimport tinyarrayimport numpy as npfrom numpy import cos, sin, >>>> piimport cmathfrom cmath import expsigma_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 systdef 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.showdef 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 >
