Hi Adel,
Running the code you provided also produces the following warning.
> UserWarning: Hamiltonian breaks Conservation law, ignoring the symmetry in
> the computation.
This should explain what is happening.
Best,
Anton
On Sun, 15 Aug 2021 at 14:19, Adel Belayadi <adelp...@gmail.com> wrote:
>
> Dear Anton;
>
> Thank you for your reply
>
> I have used the conservation_law as you have suggested. In fact, a dictionary
> or function definition of the conservation law is working fine now. I am not
> getting an error while defining the conservation law. However, when calling
> smatrix.transmission((1, 1), (0, 1)) which stands for spin up-up
> transmittance it raises: index 2 is out of bounds for axis 0 with size 2.
>
> Please see for example the following script which have two site families, one
> with 2 orbitals and the second with 6 orbitals
>
> Cheers, Adel
>
>
> import kwant
> from matplotlib import pyplot
> import numpy as np
> from math import sqrt
> lat = kwant.lattice.honeycomb(a=1, norbs=[2, 6] , name=["a", "b"])
> a, b =lat.sublattices
> def make_sys(l, w, cons_law):
> def rect(pos):
> x, y = pos
> return abs(x) < l and abs(y) < w
> sys=kwant.Builder()
> sys[a.shape(rect, (0, 0))] = np.eye(2)
> sys[b.shape(rect, (0, 0))] = np.eye(6)
> ab_hopps= (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b))
> sys[[kwant.builder.HoppingKind(*hopping) for hopping in ab_hopps]] =
> np.eye(2,6)
> sys.eradicate_dangling()
> sys[a.neighbors(1)] = np.eye(2)
> sys[b.neighbors(1)] = np.eye(6)
> ### creating leads
> def lead_shape(pos):
> x, y = pos
> return abs(y)< w
> sym = kwant.TranslationalSymmetry(lat.vec((-1, 0)))
> sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)])
> sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)])
> lead = kwant.Builder(sym, conservation_law=cons_law)
> lead[a.shape(rect, (0, 0))] = np.eye(2)
> lead[b.shape(rect, (0, 0))] = np.eye(6)
> lead[[kwant.builder.HoppingKind(*hopping) for hopping in ab_hopps]] =
> np.eye(2,6)
> lead.eradicate_dangling()
> lead[a.neighbors(1)] = np.eye(2)
> lead[b.neighbors(1)] = np.eye(6)
> sys.attach_lead(lead)
> sys.attach_lead(lead.reversed())
> return sys
>
>
> syst = make_sys(l=3, w=2, cons_law= None)
> kwant.plot(syst ,fig_size=(8, 8))
> pyplot.show()
>
> print('************ calling the conservation law **************')
> sigma_z = np.array([[1, 0], [0, -1]])
> cons_law = {a: -sigma_z , b: -np.kron(sigma_z, np.eye(3))}
> syst = make_sys(l=3, w=2, cons_law=cons_law)
> smatrix = kwant.smatrix(syst.finalized(), 0.01)
> total_trans = smatrix.transmission(1, 0)
> up_up_trans = smatrix.transmission((1, 0), (0, 0))
> dn_dn_trans = smatrix.transmission((1, 1), (0, 1))
> up_dn_trans = smatrix.transmission((1, 1), (0, 0))
> dn_up_trans = smatrix.transmission((1, 0), (0, 1))
> print(total_trans)
> print(up_up_trans)
> print(dn_dn_trans)
> print(up_dn_trans)
> print(dn_up_trans)
> print(round(total_trans,
> 3)==round(up_up_trans+dn_dn_trans+up_dn_trans+dn_up_trans, 3))
>
>
>
> Le sam. 14 août 2021 à 17:06, Anton Akhmerov <anton.akhmerov...@gmail.com> a
> écrit :
>>
>> Hi Adel,
>>
>> Please check the documentation [1]. Since you have multiple site
>> families, you need to specify the conservation law as a dictionary, so
>> {metal_like_sub: -np.kron(sigma_z, np.eye(3)), C_like_sub1: -sigma_z,
>> C_like_sub2: -sigma_z}.
>>
>> Best,
>> Anton
>>
>> https://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwant.builder.Builder
>>
>> On Sat, 14 Aug 2021 at 16:08, Adel Belayadi <adelp...@gmail.com> wrote:
>> >
>> > Dear Kwant user,
>> > Good day and I hope this email finds you well.
>> > Using conservation law was fully explained, in the Kwant mailing list,
>> > while we are having sublattices with the same degree of freedom (same
>> > number of orbitals). For instance, if we have two sites with 3 orbitals in
>> > the case of a spin full Hamiltonian, the onsite matrix is
>> > (onsite_matrix(6*6) for each site ). So in this case, the conservation
>> > law will be straightforward: conservation_law=-np.kron(sigma_z,
>> > np.eye(3)).But what would be the case if we are dealing with sublattices
>> > which have different numbers of orbitals?
>> >
>> > In my case, I am interested in spin conductance. I am using 3 sublattices
>> > with different orbitals. Let us say for instance
>> > sublattice0 has (6-orbitals), sublattice1 with (2-orbitals) and
>> > sublattice2 with (2-orbitals). In fact I am working on hetero-structure
>> > with two sites of C-like(pz with spin up and down) and one site of
>> > metal-like(3d-orbitals with spin up and down). I can resume my lattice as
>> > follow
>> >
>> > lat = kwant.lattice.general(prim_vecs, basis=[ [...], [...], [...]] ,
>> > norbs=[6, 2, 2])
>> > metal-like_sub, C-like_sub1, C-like_sub2 = lat.sublattices
>> >
>> > According to my understanding the conservation law would be something like
>> > conservation_law=-np.kron(sigma_z, np.eye(5)). However Kwant raises an
>> > error with my choice of the conservation law.
>> >
>> > Is there something missing with my understanding of the conservation law!.
>> > Or in the case of different orbitals per site, we need to define two
>> > lattices (lattice1 for spin up and lattice2 for spindown).
>> > Thanks in advance,
>> > Best
>> >
>> >
>> >
