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 <adelphys@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+kd@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 <adelphys@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
>> >
>> >
>> >