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
