def test_opservables_spin():
def onsite(site, B):
return 2 * np.eye(2) + B * sigmaz
L = 20
lat = kwant.lattice.chain(norbs=2)
syst = kwant.Builder()
syst[(lat(i) for i in range(L))] = onsite
syst[lat.neighbors()] = -1 * np.eye(2)
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, )))
lead[lat(0)] = onsite
lead[lat.neighbors()] = -1 * np.eye(2)
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
args = (0.1, )
down, up = kwant.wave_function(fsyst, energy=1., args=args)(0)
x_hoppings = kwant.builder.HoppingKind((1, ), lat)
spin_current_z = ops.Current(fsyst, sigmaz, where=x_hoppings(syst))
_test(spin_current_z, up, args=args, per_el_val=1)
_test(spin_current_z, down, args=args, per_el_val=-1)
# calculate spin_x torque
spin_torque_x = ops.Source(fsyst, sigmax, where=[lat(L // 2)])
i = fsyst.id_by_site[lat(L // 2)]
psi = up[2 * i:2 * (i + 1)] + down[2 * i:2 * (i + 1)]
H_ii = onsite(None, *args)
K = np.dot(H_ii, sigmax) - np.dot(sigmax, H_ii)
expect = 1j * ft.reduce(np.dot, (psi.conj(), K, psi))
_test(spin_torque_x, up + down, args=args, reduced_val=expect)
def test_opservables_finite():
lat, syst = _random_square_system(3)
fsyst = syst.finalized()
ev, wfs = la.eigh(fsyst.hamiltonian_submatrix())
Q = ops.Density(fsyst)
Qtot = ops.Density(fsyst, sum=True)
J = ops.Current(fsyst)
K = ops.Source(fsyst)
for i, wf in enumerate(wfs.T): # wfs[:, i] is i'th eigenvector
assert np.allclose(Q.act(wf), wf) # this operation is identity
_test(Q, wf, reduced_val=1) # eigenvectors are normalized
_test(Qtot, wf, per_el_val=1) # eigenvectors are normalized
_test(J, wf, per_el_val=0) # time-reversal symmetry: no current
_test(K, wf, per_el_val=0) # onsite commutes with hamiltonian
# check that we get correct (complex) output
for bra, ket in zip(wfs.T, wfs.T):
_test(Q, bra, ket, per_el_val=(bra * ket))
# check with get_hermiticity=False
Qi = ops.Density(fsyst, 1j, check_hermiticity=False)
for wf in wfs.T: # wfs[:, i] is i'th eigenvector
assert np.allclose(Qi.act(wf), 1j * wf)
# test with different numbers of orbitals
lat2 = kwant.lattice.chain(norbs=2)
extra_sites = [lat2(i) for i in range(len(fsyst.sites))]
syst[extra_sites] = np.eye(2)
syst[zip(fsyst.sites, extra_sites)] = ta.matrix([1, 1])
fsyst = syst.finalized()
ev, wfs = la.eigh(fsyst.hamiltonian_submatrix())
Q = ops.Density(fsyst)
Qtot = ops.Density(fsyst, sum=True)
J = ops.Current(fsyst)
K = ops.Source(fsyst)
for wf in wfs.T: # wfs[:, i] is i'th eigenvector
assert np.allclose(Q.act(wf), wf) # this operation is identity
_test(Q, wf, reduced_val=1) # eigenvectors are normalized
_test(Qtot, wf, per_el_val=1) # eigenvectors are normalized
_test(J, wf, per_el_val=0) # time-reversal symmetry: no current
_test(K, wf, per_el_val=0) # onsite commutes with hamiltonian