Re: [Kwant] Plotting energy as a function of magnetic field in 3D.
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 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 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 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) >>>
Re: [Kwant] Plotting energy as a function of magnetic field in 3D.
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 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
> 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
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>> *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_zdef 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_ydef 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))] = onsitesyst[kwant.builder.HoppingKind((1,
>> 0, 0), lat, lat)] = hoppingzsyst[kwant.builder.HoppingKind((0, 1, 0),
>> lat, lat)] = hoppingysyst[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))]=onsitelead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
>> = hoppingzlead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
>> hoppingylead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
>> hoppingxsyst.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))]=onsitelead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
>> = hoppingzlead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
>> hoppingylead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
>> hoppingxsyst.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 * 0.2 for B in range(101)])main()*
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>> Naveen
>> Department of Physics & Astrophysics
>> University of Delhi
>> New Delhi-110007
>>
>> On Sun, Sep 8, 2019, 17:37 Abbout Adel 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
