def test_MultiCouplingModel_explicit():
fermion_lat_cyl = lattice.Square(1,
2,
fermion_site,
bc='periodic',
bc_MPS='infinite')
M = model.MultiCouplingModel(fermion_lat_cyl)
# create a wired fermionic model with 3-body interactions
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1))
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), 'JW')
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), 'JW')
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), 'JW')
M.add_multi_coupling(4., 0, 'N', [(0, 'N', (2, 1))],
'Id') # a full unit cell inbetween!
# some wired mediated hopping along the diagonal
M.add_multi_coupling(1.125,
0,
'N',
other_ops=[(0, 'Cd', (0, 1)), (0, 'C', (1, 0))])
H_mpo = M.calc_H_MPO()
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
W2_new = H_mpo.get_W(2)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW)
JWC = JW.matvec(C)
NJW = N.matvec(JW)
# yapf: disable
W0_ex = [[Id, None, None, CdJW, None, JWC, N, None, None, None, N*0.125],
[None, None, Id, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, JW, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, Id, None, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, C*1.125],
[None, None, None, None, None, None, None, JW, None, None, None],
[None, None, None, None, None, None, None, None, JW, None, None],
[None, None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, None, None, None, None, None, None, CdJW, JWC, N, N*0.125],
[None, Id, None, None, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, JW, NJW, None, None, None, None, None, None, C*0.5],
[None, None, None, None, None, None, None, None, None, None, None, C*1.125],
[None, None, None, None, None, JW, None, None, None, None, None, Cd*0.5],
[None, None, None, None, None, None, Id, CdJW, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, None, Id, None, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W0_new -
W0_ex) == 0. # coupling constants: no rounding errors
assert npc.norm(W1_new -
W1_ex) == 0. # coupling constants: no rounding errors
def test_model_H_conversion(L=6):
bc = 'finite'
model_params = {'L': L, 'hz': np.random.random([L]), 'bc_MPS': bc}
m = XXZChain(model_params)
# can we run the conversion?
# conversion from bond to MPO in NearestNeighborModel
H_MPO = m.calc_H_MPO_from_bond()
# conversion from MPO to bond in MPOModel
H_bond = m.calc_H_bond_from_MPO()
# compare: did we get the correct result?
ED = ExactDiag(m)
ED.build_full_H_from_bonds()
H0 = ED.full_H # this should be correct
ED.full_H = None
m.H_MPO = H_MPO
ED.build_full_H_from_mpo()
full_H_mpo = ED.full_H # the one generated by NearstNeighborModel.calc_H_MPO_from_bond()
print("npc.norm(H0 - full_H_mpo) = ", npc.norm(H0 - full_H_mpo))
assert npc.norm(H0 -
full_H_mpo) < 1.e-14 # round off errors on order of 1.e-15
m.H_bond = H_bond
ED.full_H = None
ED.build_full_H_from_bonds()
full_H_bond = ED.full_H # the one generated by NearstNeighborModel.calc_H_MPO_from_bond()
print("npc.norm(H0 - full_H_bond) = ", npc.norm(H0 - full_H_bond))
assert npc.norm(
H0 - full_H_bond) < 1.e-14 # round off errors on order of 1.e-15
def make_uniform(psi):
_chis = psi.chi
#RCF
TB = TransferMatrix(psi, psi, shift_bra=1, shift_ket=0)
es_B, evs_B = TB.eigenvectors()
U = evs_B[0].split_legs(['(vL.vL*)']).iset_leg_labels(['vL','vR'])
_B = psi.get_B(1)
B = npc.tensordot(_B, U, axes=('vR','vL'))
B = (B/npc.norm(B))*np.sqrt(_chis[1])
#LCF
TA = TransferMatrix(psi, psi, shift_bra=1, shift_ket=0, form='A', transpose=True)
es_A, evs_A = TA.eigenvectors()
V = evs_A[0].split_legs(['(vR*.vR)'])
Vdag = V.conj()
_A = psi.get_B(1, form='A')
A = npc.tensordot(_A, Vdag, axes=('vR','vR*'))
A = (A/npc.norm(A))*np.sqrt(_chis[1])
s = 0.5*(psi.get_SL(0) + psi.get_SL(1))
upsi = make_uMPS(psi)
upsi.set_B(0, A, form='A')
upsi.set_B(0, B)
upsi.set_SL(0, s)
return upsi
def test_CouplingModel_multi_couplings_explicit(use_plus_hc, JW):
fermion_lat_cyl = lattice.Square(1,
2,
fermion_site,
bc='periodic',
bc_MPS='infinite')
M = model.CouplingModel(fermion_lat_cyl)
# create a wired fermionic model with 3-body interactions
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1), plus_hc=use_plus_hc)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), JW, plus_hc=use_plus_hc)
if not use_plus_hc:
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), JW)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), JW)
# multi_coupling with a full unit cell inbetween the operators!
M.add_multi_coupling(4., [('N', (0, 0), 0), ('N', (-2, -1), 0)])
# some wired mediated hopping along the diagonal
M.add_multi_coupling(1.125, [('N', (0, 0), 0), ('Cd', (0, 1), 0),
('C', (1, 0), 0)])
H_mpo = M.calc_H_MPO()
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW) # = Cd
CJW = C.matvec(JW) # = -C
NJW = N.matvec(JW)
# print(M.H_MPO_graph._build_grids())
# yapf: disable
W0_ex = [[Id, CJW, CdJW, None, N, None, None, None, None, None, N*0.125],
[None, None, None, None, None, None, None, None, None, None, Cd*-1.5],
[None, None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, JW, None, None, None, None, None, None, None],
[None, None, None, None, None, Id, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, C*1.125],
[None, None, None, None, None, None, Id, None, None, None, None],
[None, None, None, None, None, None, None, JW, None, None, None],
[None, None, None, None, None, None, None, None, JW, None, None],
[None, None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, None, None, None, None, None, CJW, CdJW, N, None, N*0.125],
[None, JW, None, None, None, None, None, None, None, None, None, Cd*-0.5],
[None, None, JW, NJW, None, None, None, None, None, None, None, C*0.5],
[None, None, None, None, None, None, None, None, None, None, None, C*1.125],
[None, None, None, None, Id, CdJW, None, None, None, None, None, None],
[None, None, None, None, None, None, Id, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, None, None, Cd*-1.5],
[None, None, None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W0_new -
W0_ex) == 0. # coupling constants: no rounding errors
assert npc.norm(W1_new -
W1_ex) == 0. # coupling constants: no rounding errors
def calculate_error_left_right(self, i):
Lp = self.environment.get_LP(i)
Rp = self.environment.get_RP(i)
W = self.H_MPO.get_W(i)
B = self.psi.get_B(i)
p_h_phi = npc.tensordot(Lp, W, axes=['wR', 'wL'])
p_h_phi = npc.tensordot(p_h_phi, Rp, axes=['wR', 'wL'])
p_h_phi = npc.tensordot(p_h_phi,
B,
axes=[('p*', 'vR', 'vL'), ('p', 'vL', 'vR')])
npc.norm(p_h_phi)
def test_random_matrix_CUE():
for size in [1, 3, 4]:
a = rmat.CUE((size, size))
print(a)
assert (a.dtype == np.complex)
npt.assert_allclose(np.dot(a, a.T.conj()), np.eye(size), EPS, EPS)
b = npc.Array.from_func_square(rmat.CUE, leg)
b.test_sanity()
assert (b.dtype == np.complex)
print("b =", b)
id = npc.eye_like(b)
assert (npc.norm(npc.tensordot(b, b.conj().itranspose(), axes=[1, 0]) - id) < EPS)
assert (npc.norm(npc.tensordot(b.conj().itranspose(), b, axes=[1, 0]) - id) < EPS)
def test_CouplingModel_explicit():
fermion_lat_cyl = lattice.Square(1,
2,
fermion_site,
bc='periodic',
bc_MPS='infinite')
M = model.CouplingModel(fermion_lat_cyl)
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1),
None) # auto-determine JW-string!
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), None)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), None)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), None)
M.add_coupling(4., 0, 'N', 0, 'N', (-2, -1),
None) # a full unit cell inbetween!
H_mpo = M.calc_H_MPO()
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW) # = Cd
CJW = C.matvec(JW) # = -C
# yapf: disable
W0_ex = [[Id, CJW, CdJW, N, None, None, None, None, None, N*0.125],
[None, None, None, None, None, None, None, None, None, Cd*-1.5],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, Id, None, None, None, None, None],
[None, None, None, None, None, Id, None, None, None, None],
[None, None, None, None, None, None, JW, None, None, None],
[None, None, None, None, None, None, None, JW, None, None],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, None, None, None, CJW, CdJW, N, None, N*0.125],
[None, JW, None, None, None, None, None, None, None, Cd*-0.5],
[None, None, JW, None, None, None, None, None, None, C*0.5],
[None, None, None, Id, None, None, None, None, None, None],
[None, None, None, None, Id, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, Cd*-1.5],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W0_new -
W0_ex) == 0. # coupling constants: no rounding errors
assert npc.norm(W1_new -
W1_ex) == 0. # coupling constants: no rounding errors
def test_CouplingModel_explicit():
fermion_lat_cyl = lattice.SquareLattice(1,
2,
fermion_site,
bc_MPS='infinite')
M = model.CouplingModel(fermion_lat_cyl, 'periodic')
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1), 'JW')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), 'JW')
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), 'JW')
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), 'JW')
M.add_coupling(4., 0, 'N', 0, 'N', (2, 1),
'Id') # a full unit cell inbetween!
H_mpo = M.calc_H_MPO()
# MPO should be translation invariant!
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW)
JWC = JW.matvec(C)
# yapf: disable
W0_ex = [[Id, None, None, CdJW, JWC, N, None, None, None, N*0.125],
[None, None, Id, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, Id, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, JW, None, None, None],
[None, None, None, None, None, None, None, JW, None, None],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, None, None, None, None, CdJW, JWC, N, N*0.125],
[None, Id, None, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, JW, None, None, None, None, None, C*0.5],
[None, None, None, None, JW, None, None, None, None, Cd*0.5],
[None, None, None, None, None, Id, None, None, None, None],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, None, Id, None, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W0_new -
W0_ex) == 0. # coupling constants: no rounding errors
assert npc.norm(W1_new -
W1_ex) == 0. # coupling constants: no rounding errors
def test_FlatHermitianOperator(n=30, k=5, tol=5.e-15):
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg)
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [leg])
H_sparse = sparse.FlatHermitianOperator.from_NpcArray(H,
charge_sector=qtotal)
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init_flat = H_sparse.npc_to_flat(psi_init)
# check diagonalization
E, psi = scipy.sparse.linalg.eigsh(H_sparse,
k,
v0=psi_init_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
def test_random_matrix_U_close_1():
for x in [0., 0.001]:
for size in [1, 3, 4]:
a = rmat.U_close_1((size, size), x)
print(a)
assert (a.dtype == np.complex)
npt.assert_allclose(np.dot(a, a.T.conj()), np.eye(size), EPS, EPS)
npt.assert_allclose(a, np.eye(size), 10 * x, 10 * x + EPS) # not exact for x=0!
b = npc.Array.from_func_square(rmat.U_close_1, leg, func_args=[x])
b.test_sanity()
assert (b.dtype == np.complex)
print("b =", b)
id = npc.eye_like(b)
assert (npc.norm(npc.tensordot(b, b.conj().itranspose(), axes=[1, 0]) - id) < EPS)
assert (npc.norm(npc.tensordot(b.conj().itranspose(), b, axes=[1, 0]) - id) < EPS)
assert (npc.norm(b - id) <= 10 * x + EPS) # not exact for x=0!
def test_ED():
# just quickly check that it runs without errors for a small system
xxz_pars = dict(L=4, Jxx=1., Jz=1., hz=0.0, bc_MPS='finite')
M = XXZChain(xxz_pars)
ED = ExactDiag(M)
ED.build_full_H_from_mpo()
H, ED.full_H = ED.full_H, None
ED.build_full_H_from_bonds()
H2 = ED.full_H
assert (npc.norm(H - H2, np.inf) < 1.e-14)
ED.full_diagonalization()
psi = ED.groundstate()
print("select charge_sector =", psi.qtotal)
ED2 = ExactDiag(M, psi.qtotal)
ED2.build_full_H_from_mpo()
ED2.full_diagonalization()
psi2 = ED2.groundstate()
full_psi2 = psi.zeros_like()
full_psi2[ED2._mask] = psi2
ov = npc.inner(psi, full_psi2, do_conj=True)
print("overlab <psi | psi2> = 1. -", 1. - ov)
assert (abs(abs(ov) - 1.) < 1.e-15)
# starting from a random guess in the correct charge sector,
# check if we can also do lanczos.
np.random.seed(12345)
psi3 = npc.Array.from_func(np.random.random,
psi2.legs,
qtotal=psi2.qtotal,
shape_kw='size')
E0, psi3, N = lanczos(ED2, psi3)
print("Lanczos E0 =", E0)
ov = npc.inner(psi3, psi2, do_conj=True)
print("overlab <psi2 | psi3> = 1. -", 1. - ov)
assert (abs(abs(ov) - 1.) < 1.e-15)
def test_qr():
for shape in [(4, 4), (6, 8), (8, 6)]:
tol = shape[0] * shape[1] * 100
for qtotal_A in [None, [1]]:
A = random_Array(shape, chinfo3, qtotal=qtotal_A, sort=False)
A_flat = A.to_ndarray()
for qtotal_Q in [None, [1]]:
for mode in ['reduced', 'complete']:
for qconj in [+1, -1]:
for pos in [False, True]:
print(
f"shape={shape!s} qtot_A={qtotal_A!s} qtot_Q={qtotal_Q!s}"
f"mode={mode!s} pos_diag_R={pos!s} inner_qconj={qconj:+d}"
)
Q, R = npc.qr(A,
mode=mode,
pos_diag_R=pos,
qtotal_Q=qtotal_Q,
inner_qconj=qconj)
# print(q._qdata)
Q.test_sanity()
R.test_sanity()
assert np.all(
Q.qtotal) == A.chinfo.make_valid(qtotal_Q)
assert R.legs[0].qconj == qconj
QR = npc.tensordot(Q, R, axes=1)
npt.assert_array_almost_equal_nulp(
A_flat, QR.to_ndarray(), tol)
QdaggerQ = npc.tensordot(Q.conj(), Q, axes=[0, 0])
assert npc.norm(QdaggerQ -
npc.eye_like(QdaggerQ)) < 1.e-10
def test_eig():
size = 10
max_nulp = 10 * size**3
ci = chinfo3
l = gen_random_legcharge(ci, size)
A = npc.Array.from_func(np.random.random, [l, l.conj()],
qtotal=None,
shape_kw='size')
print("hermitian A")
A += A.conj().itranspose()
Aflat = A.to_ndarray()
W, V = npc.eigh(A, sort='m>')
V.test_sanity()
V_W = V.scale_axis(W, axis=-1)
recalc = npc.tensordot(V_W, V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Aflat, recalc.to_ndarray(), max_nulp)
Wflat, Vflat = np.linalg.eigh(Aflat)
npt.assert_array_almost_equal_nulp(np.sort(W), Wflat, max_nulp)
W2 = npc.eigvalsh(A, sort='m>')
npt.assert_array_almost_equal_nulp(W, W2, max_nulp)
print("check complex B")
B = 1.j * npc.Array.from_func(np.random.random, [l, l.conj()],
shape_kw='size')
B += B.conj().itranspose()
B = A + B
Bflat = B.to_ndarray()
W, V = npc.eigh(B, sort='m>')
V.test_sanity()
recalc = npc.tensordot(V.scale_axis(W, axis=-1), V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Bflat, recalc.to_ndarray(), max_nulp)
Wflat, Vflat = np.linalg.eigh(Bflat)
npt.assert_array_almost_equal_nulp(np.sort(W), Wflat, max_nulp)
print("calculate without 'hermitian' knownledge")
W, V = npc.eig(B, sort='m>')
assert (np.max(np.abs(W.imag)) < EPS * max_nulp)
npt.assert_array_almost_equal_nulp(np.sort(W.real), Wflat, max_nulp)
print("sparse speigs")
qi = 1
ch_sect = B.legs[0].get_charge(qi)
k = min(3, B.legs[0].slices[qi + 1] - B.legs[0].slices[qi])
Wsp, Vsp = npc.speigs(B, ch_sect, k=k, which='LM')
for W_i, V_i in zip(Wsp, Vsp):
V_i.test_sanity()
diff = npc.tensordot(B, V_i, axes=1) - V_i * W_i
assert (npc.norm(diff, np.inf) < EPS * max_nulp)
print("for trivial charges")
A = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()],
shape_kw='size')
A = A + A.conj().itranspose()
Aflat = A.to_ndarray()
W, V = npc.eigh(A)
recalc = npc.tensordot(V.scale_axis(W, axis=-1), V.conj(), axes=[1, 1])
npt.assert_array_almost_equal_nulp(Aflat, recalc.to_ndarray(),
10 * A.shape[0]**3)
def test_npc_addition_transpose():
# addition with labels and transposed axes
a1 = np.random.random([3, 3, 4])
a2 = np.swapaxes(a1, 0, 1)
t1 = npc.Array.from_ndarray_trivial(a1, labels=['a', 'b', 'c'])
t2 = npc.Array.from_ndarray_trivial(a2, labels=['b', 'a', 'c'])
# TODO: for now warning
with pytest.warns(FutureWarning):
diff = npc.norm(t1 - t2)
def test_npc_Array_norm():
a = random_Array((15, 10), chinfo3, sort=True)
aflat = a.to_ndarray()
for ord in [np.inf, -np.inf, 0, 1, 2, 3.]: # divides by 0 for neg. ord
print("ord = ", ord)
anorm = a.norm(ord)
aflnorm = npc.norm(aflat, ord)
print(abs(anorm - aflnorm))
assert (abs(anorm - aflnorm) < 100 * EPS)
def test_random_matrix_GUE():
for size in [1, 3, 4]:
a = rmat.GUE((size, size))
assert (a.dtype == np.complex)
print(a)
npt.assert_array_equal(a, a.T.conj())
b = npc.Array.from_func_square(rmat.GUE, leg)
b.test_sanity()
assert (b.dtype == np.complex)
print("b =", b)
assert (npc.norm(b - b.conj().itranspose()) == 0)
def test_npc_tensordot_extra():
# check that the sorting of charges is fine with special test matrices
# which gave me some headaches at some point :/
chinfo = npc.ChargeInfo([1], ['Sz'])
leg = npc.LegCharge.from_qflat(chinfo, [-1, 1])
legs = [leg, leg, leg.conj(), leg.conj()]
idx = [(0, 0, 0, 0), (0, 1, 0, 1), (0, 1, 1, 0), (1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 1, 1)]
Uflat = np.eye(4).reshape([2, 2, 2, 2]) # up to numerical rubbish the identity
Uflat[0, 1, 1, 0] = Uflat[1, 0, 0, 1] = 1.e-20
U = npc.Array.from_ndarray(Uflat, legs, cutoff=0.)
theta_flat = np.zeros([2, 2, 2, 2])
vals = np.random.random(len(idx))
vals /= np.linalg.norm(vals)
for i, val in zip(idx, vals):
theta_flat[i] = val
theta = npc.Array.from_ndarray(theta_flat, [leg, leg, leg.conj(), leg.conj()], cutoff=0.)
assert abs(np.linalg.norm(theta_flat) - npc.norm(theta)) < 1.e-14
Utheta_flat = np.tensordot(Uflat, theta_flat, axes=2)
Utheta = npc.tensordot(U, theta, axes=2)
npt.assert_array_almost_equal_nulp(Utheta.to_ndarray(), Utheta_flat, 10)
assert abs(np.linalg.norm(theta_flat) - npc.norm(Utheta)) < 1.e-10
def test_XXZChain_general(tol=1.e-14):
check_general_model(XXZChain, dict(L=4, Jxx=1., hz=0., bc_MPS='finite'), {
'Jz': [0., 1., 2.],
'hz': [0., 0.2]
})
model_param = dict(L=3, Jxx=1., Jz=1.5, hz=0.25, bc_MPS='finite')
m1 = XXZChain(model_param)
m2 = XXZChain2(model_param)
for Hb1, Hb2 in zip(m1.H_bond, m2.H_bond):
if Hb1 is None:
assert Hb2 is None
continue
assert npc.norm(Hb1 - Hb2) < tol
def check_model_sanity(M, hermitian=True):
"""call M.test_sanity() for all different subclasses of M"""
if isinstance(M, model.CouplingModel):
model.CouplingModel.test_sanity(M)
if isinstance(M, model.NearestNeighborModel):
model.NearestNeighborModel.test_sanity(M)
if hermitian:
for i, H in enumerate(M.H_bond):
if H is not None:
err = npc.norm(H - H.conj().transpose(H.get_leg_labels()))
if err > 1.e-14:
print(H)
raise ValueError("H on bond {i:d} not hermitian".format(i=i))
if isinstance(M, model.MPOModel):
model.MPOModel.test_sanity(M)
test_mpo.check_hermitian(M.H_MPO)
def test_XXZChain():
pars = dict(L=4, Jxx=1., Jz=1., hz=0., bc_MPS='finite')
chain = XXZChain(pars)
chain.test_sanity()
for Hb in chain.H_bond[1:]: # check bond eigenvalues
Hb2 = Hb.combine_legs([['p0', 'p1'], ['p0*', 'p1*']], qconj=[+1, -1])
print(Hb2.to_ndarray())
W = npc.eigvalsh(Hb2)
npt.assert_array_almost_equal_nulp(np.sort(W),
np.sort([-0.75, 0.25, 0.25, 0.25]),
16**3)
# now check with non-trivial onsite terms
pars['hz'] = 0.2
print("hz =", pars['hz'])
chain = XXZChain(pars)
chain.test_sanity()
Hb = chain.H_bond[
2] # the only central bonds: boundaries have different hz.
Hb2 = Hb.combine_legs([['p0', 'p1'], ['p0*', 'p1*']], qconj=[+1, -1])
print(Hb2.to_ndarray())
W = npc.eigvalsh(Hb2)
print(W)
npt.assert_array_almost_equal_nulp(
np.sort(W),
np.sort([
-0.75, 0.25 - 2 * 0.5 * 0.5 * pars['hz'], 0.25,
0.25 + 2. * 0.5 * 0.5 * pars['hz']
]), 16**3)
pars['bc_MPS'] = 'infinite'
for L in [2, 3, 4, 5, 6]:
print("L =", L)
pars['L'] = L
chain = XXZChain(pars)
pprint.pprint(chain.coupling_terms)
assert len(chain.H_bond) == L
Hb0 = chain.H_bond[0]
for Hb in chain.H_bond[1:]:
assert (npc.norm(Hb - Hb0, np.inf) == 0.) # exactly equal
pars['Jxx'] = 0.
chain = XXZChain(pars)
chain.test_sanity()
def sweep_right_left_two(self):
"""Performs the sweep left->right of the second order TDVP scheme with two sites update.
Evolve from 0.5*dt
"""
theta_old = self.psi.get_theta(self.L - 1, 1)
for j in range(self.L - 2, -1, -1):
theta = npc.tensordot(theta_old, self.psi.get_B(j, form='A'),
('vL', 'vR'))
theta.ireplace_label('p0', 'p1')
theta.ireplace_label('p', 'p0')
#theta=self.psi.get_theta(j,2)
Lp = self.environment.get_LP(j)
Rp = self.environment.get_RP(j + 1)
W1 = self.environment.H.get_W(j)
W2 = self.environment.H.get_W(j + 1)
theta = self.update_theta_h2(Lp, Rp, theta, W1, W2,
-1j * 0.5 * self.dt)
theta = theta.combine_legs([['vL', 'p0'], ['vR', 'p1']],
qconj=[+1, -1])
# SVD and update environment
U, s, V, err, renorm = svd_theta(theta, self.trunc_params)
s = s / npc.norm(s)
U = U.split_legs('(vL.p0)')
U.ireplace_label('p0', 'p')
V = V.split_legs('(vR.p1)')
V.ireplace_label('p1', 'p')
self.psi.set_B(j, U, form='A')
self._del_correct(j)
self.psi.set_SR(j, s)
self.psi.set_B(j + 1, V, form='B')
self._del_correct(j + 1)
if j > 0:
# Apply expm (-dt H) for 1-site
theta = self.psi.get_theta(j, 1)
theta.ireplace_label('p0', 'p')
Lp = self.environment.get_LP(j)
Rp = self.environment.get_RP(j)
theta = self.update_theta_h1(Lp, Rp, theta, W1,
1j * 0.5 * self.dt)
theta_old = theta
theta.ireplace_label('p', 'p0')
def assert_equal_data(data_imported, data_expected, max_recursion_depth=10):
"""Check that the imported data is as expected."""
assert isinstance(data_imported, type(data_expected))
if hasattr(data_expected, 'test_sanity'):
data_imported.test_sanity()
if isinstance(data_expected, dict):
assert set(data_imported.keys()) == set(data_expected.keys())
if max_recursion_depth > 0:
for ki in data_imported.keys():
assert_equal_data(data_imported[ki], data_expected[ki], max_recursion_depth - 1)
elif isinstance(data_expected, (list, tuple)):
if max_recursion_depth > 0:
for vi, ve in zip(data_imported, data_expected):
assert_equal_data(vi, ve, max_recursion_depth - 1)
elif isinstance(data_expected, npc.Array):
assert npc.norm(data_imported - data_expected) == 0. # should be exactly equal!
elif isinstance(data_expected, np.ndarray):
np.testing.assert_array_equal(data_imported, data_expected)
elif isinstance(data_expected, (int, float, np.int64, np.float64, complex, str)):
assert data_imported == data_expected
def test_lanczos_evolve(n, N_cache, tol=5.e-14):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
#psi_init /= npc.norm(psi_init) # not necessary
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {'N_cache': N_cache})
for delta in [-0.1j, 0.1j, 1.j, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
norm = np.linalg.norm(psi_final_flat)
psi_final, N = lanc.run(delta, normalize=False)
diff = np.linalg.norm(psi_final.to_ndarray() - psi_final_flat)
print("norm(|psi_final> - |psi_final_flat>)/norm = ",
diff / norm) # should be 1.
assert diff / norm < tol
psi_final2, N = lanc.run(delta, normalize=True)
assert npc.norm(psi_final / norm - psi_final2) < tol
def test_lanczos_evolve(n, N_cache, tol=5.e-15):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {
'verbose': 1,
'N_cache': N_cache
})
for delta in [-0.1j, 0.1j, 1.j]: #, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
psi_final, N = lanc.run(delta)
ov = np.inner(psi_final.to_ndarray().conj(), psi_final_flat)
ov /= np.linalg.norm(psi_final_flat)
print("<psi1|psi1_flat>/norm=", ov)
assert (abs(1. - abs(ov)) < tol)
def test_MPO_conversion():
L = 8
sites = []
for i in range(L):
s = site.Site(spin_half.leg)
s.add_op("X_{i:d}".format(i=i), np.diag([2., 1.]))
s.add_op("Y_{i:d}".format(i=i), np.diag([1., 2.]))
sites.append(s)
terms = [
[("X_0", 0)],
[("X_0", 0), ("X_1", 1)],
[("X_0", 0), ("X_3", 3)],
[("X_4", 4), ("Y_5", 5), ("Y_7", 7)],
[("X_4", 4), ("Y_5", 5), ("X_7", 7)],
[("X_4", 4), ("Y_6", 6), ("Y_7", 7)],
]
prefactors = [0.25, 10., 11., 101., 102., 103.]
term_list = TermList(terms, prefactors)
g1 = mpo.MPOGraph.from_term_list(term_list,
sites,
bc='finite',
insert_all_id=False)
ct_add = MultiCouplingTerms(L)
ct_add.add_coupling_term(12., 4, 5, "X_4", "X_5")
ct_add.add_multi_coupling_term(0.5, [4, 5, 7], ["X_4", "Y_5", "X_7"], "Id")
ct_add.add_to_graph(g1)
H1 = g1.build_MPO()
grids = [
[['Id', 'X_0', [('X_0', 0.25)]] # site 0
],
[
['Id', None, None], # site 1
[None, 'Id', [('X_1', 10.0)]],
[None, None, 'Id']
],
[
['Id', None, None], # site 2
[None, [('Id', 11.0)], None],
[None, None, 'Id']
],
[
['Id', None], # site 3
[None, 'X_3'],
[None, 'Id']
],
[
['X_4', None], #site 4
[None, 'Id']
],
[
['Id', 'Y_5', [('X_5', 12.0)]], # site 5
[None, None, 'Id']
],
[
# site 6
[None, [('Y_6', 103.0)], None],
[[('Id', 102.5)], [('Id', 101.0)], None],
[None, None, 'Id']
],
[
['X_7'], # site 7
['Y_7'],
['Id']
]
]
H2 = mpo.MPO.from_grids(sites, grids, 'finite', [0] * 4 + [None] * 5,
[None] * 5 + [-1] * 4)
for w1, w2 in zip(H1._W, H2._W):
assert npc.norm(w1 - w2, np.inf) == 0.
pass
def test_CouplingModel_explicit():
fermion_lat_cyl = lattice.Square(1,
2,
fermion_site,
bc='periodic',
bc_MPS='infinite')
M = model.CouplingModel(fermion_lat_cyl)
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1),
None) # auto-determine JW-string!
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), None)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), None)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), None)
M.add_coupling(4., 0, 'N', 0, 'N', (-2, -1),
None) # a full unit cell inbetween!
H_mpo = M.calc_H_MPO()
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW) # = Cd
JWC = JW.matvec(C) # = C
# H_MPO_graph = tenpy.networks.mpo.MPOGraph.from_terms((M.all_onsite_terms(),
# M.all_coupling_terms(),
# M.exp_decaying_terms),
# M.lat.mps_sites(),
# M.lat.bc_MPS)
# H_MPO_graph._set_ordered_states()
# from pprint import pprint
# pprint(H_MPO_graph._ordered_states)
# print(M.all_coupling_terms().to_TermList())
# [{'IdL': 0,
# ('left', 0, 'Cd JW', 'JW'): 1,
# ('left', 0, 'JW C', 'JW'): 2,
# ('left', 0, 'N', 'Id'): 3,
# ('left', 1, 'Cd JW', 'JW'): 4,
# ('left', 1, 'JW C', 'JW'): 5,
# ('left', 1, 'N', 'Id'): 6,
# ('left', 0, 'N', 'Id', 2, 'Id', 'Id'): 7,
# ('left', 1, 'N', 'Id', 3, 'Id', 'Id'): 8},
# 'IdR': 9,
# {'IdL': 0,
# ('left', 0, 'Cd JW', 'JW'): 1,
# ('left', 0, 'JW C', 'JW'): 2,
# ('left', 0, 'N', 'Id'): 3,
# ('left', 1, 'Cd JW', 'JW'): 4,
# ('left', 1, 'JW C', 'JW'): 5,
# ('left', 1, 'N', 'Id'): 6},
# ('left', 0, 'N', 'Id', 2, 'Id', 'Id'): 7,
# ('left', 0, 'N', 'Id', 2, 'Id', 'Id', 4, 'Id', 'Id'): 8,
# 'IdR': 9,
# 0.50000 * Cd JW_0 C_1 +
# 1.50000 * Cd JW_0 C_2 +
# 0.50000 * JW C_0 Cd_1 +
# 1.50000 * JW C_0 Cd_2 +
# 4.00000 * N_0 N_5 +
# 1.50000 * Cd JW_1 C_3 +
# 1.50000 * JW C_1 Cd_3 +
# 4.00000 * N_1 N_4
# yapf: disable
W0_ex = [[Id, CdJW, JWC, N, None, None, None, None, None, N*0.125],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, None, None, None, None, None, None, Id, None, None],
[None, None, None, None, JW, None, None, None, None, None],
[None, None, None, None, None, JW, None, None, None, None],
[None, None, None, None, None, None, Id, None, None, None],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, None, None, CdJW, JWC, N, None, None, N*0.125],
[None, JW, None, None, None, None, None, None, None, C*0.5],
[None, None, JW, None, None, None, None, None, None, Cd*0.5],
[None, None, None, Id, None, None, None, None, None, None],
[None, None, None, None, None, None, None, None, None, C*1.5],
[None, None, None, None, None, None, None, None, None, Cd*1.5],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, Id, None, None],
[None, None, None, None, None, None, None, None, None, N*4.0],
[None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W0_new -
W0_ex)**2 == 0. # coupling constants: no rounding errors
assert npc.norm(W1_new -
W1_ex)**2 == 0. # coupling constants: no rounding errors
print("6) calculate exp(H2) by diagonalization of H2")
# diagonalization requires to view H2 as a matrix
H2 = H2.combine_legs([('p0', 'p1'), ('p0*', 'p1*')], qconj=[+1, -1])
print("labels after combine_legs:", H2.get_leg_labels())
E2, U2 = npc.eigh(H2)
print("Eigenvalues of H2:", E2)
U_expE2 = U2.scale_axis(np.exp(-1.j * dt * E2), axis=1) # scale_axis ~= apply a diagonal matrix
exp_H2 = npc.tensordot(U_expE2, U2.conj(), axes=(1, 1))
exp_H2.iset_leg_labels(H2.get_leg_labels())
exp_H2 = exp_H2.split_legs() # by default split all legs which are `LegPipe`
# (this restores the originial labels ['p0', 'p1', 'p0*', 'p1*'] of `H2` in `exp_H2`)
# alternative way: use :func:`~tenpy.linalg.np_conserved.expm`
exp_H2_alternative = npc.expm(-1.j * dt * H2).split_legs()
assert (npc.norm(exp_H2_alternative - exp_H2) < 1.e-14)
print("7) apply exp(H2) to even/odd bonds of the MPS and truncate with svd")
# (this implements one time step of first order TEBD)
trunc_par = {'svd_min': cutoff, 'trunc_cut': None, 'verbose': 0}
for even_odd in [0, 1]:
for i in range(even_odd, L - 1, 2):
theta = psi.get_theta(i, 2) # handles canonical form (i.e. scaling with 'S')
theta = npc.tensordot(exp_H2, theta, axes=(['p0*', 'p1*'], ['p0', 'p1']))
# view as matrix for SVD
theta = theta.combine_legs([('vL', 'p0'), ('p1', 'vR')], new_axes=[0, 1], qconj=[+1, -1])
# now theta has labels '(vL.p0)', '(p1.vR)'
U, S, V, err, invsq = svd_theta(theta, trunc_par, inner_labels=['vR', 'vL'])
psi.set_SR(i, S)
A_L = U.split_legs('(vL.p0)').ireplace_label('p0', 'p')
B_R = V.split_legs('(p1.vR)').ireplace_label('p1', 'p')
def test_FlatHermitianOperator(n=30, k=5, tol=1.e-14):
leg = gen_random_legcharge(ch, n // 2)
leg2 = gen_random_legcharge(ch, 2)
pipe = npc.LegPipe([leg, leg2], qconj=+1)
H = npc.Array.from_func_square(rmat.GUE, pipe)
H.iset_leg_labels(["(a.b)", "(a*.b*)"])
H_flat = H.to_ndarray()
E_flat, psi_flat = np.linalg.eigh(H_flat)
E0_flat, psi0_flat = E_flat[0], psi_flat[:, 0]
qtotal = npc.detect_qtotal(psi0_flat, [pipe])
H_sparse = sparse.FlatHermitianOperator.from_NpcArray(H,
charge_sector=qtotal)
psi_init = npc.Array.from_func(np.random.random, [pipe], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init.iset_leg_labels(["(a.b)"])
psi_init_flat = H_sparse.npc_to_flat(psi_init)
# check diagonalization
E, psi = scipy.sparse.linalg.eigsh(H_sparse,
k,
v0=psi_init_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
# split H to check `FlatHermitianOperator.from_guess_with_pipe`.
print("=========")
print("split legs and define separate matvec")
assert psi_init.legs[0] is pipe
psi_init_split = psi_init.split_legs([0])
H_split = H.split_legs()
def H_split_matvec(vec):
vec = npc.tensordot(H_split, vec, [["a*", "b*"], ["a", "b"]])
# TODO as additional challenge, transpose the resulting vector
return vec
H_sparse_split, psi_init_split_flat = sparse.FlatLinearOperator.from_guess_with_pipe(
H_split_matvec, psi_init_split, dtype=H_split.dtype)
# diagonalize
E, psi = scipy.sparse.linalg.eigsh(H_sparse_split,
k,
v0=psi_init_split_flat,
which='SA')
E0, psi0 = E[0], psi[:, 0]
print("full spectrum:", E_flat)
print("E0 = {E0:.14f} vs exact {E0_flat:.14f}".format(E0=E0,
E0_flat=E0_flat))
print("|E0-E0_flat| / |E0_flat| =", abs((E0 - E0_flat) / E0_flat))
assert (abs((E0 - E0_flat) / E0_flat) < tol)
psi0_H_psi0 = np.inner(psi0.conj(), H_sparse.matvec(psi0)).item()
print("<psi0|H|psi0> / E0 = 1. + ", psi0_H_psi0 / E0 - 1.)
assert (abs(psi0_H_psi0 / E0 - 1.) < tol)
def test_CouplingModel_multi_couplings_explicit(use_plus_hc, JW):
fermion_lat_cyl = lattice.Square(1,
2,
fermion_site,
bc='periodic',
bc_MPS='infinite')
M = model.CouplingModel(fermion_lat_cyl)
# create a weird fermionic model with 3-body interactions
M.add_onsite(0.125, 0, 'N')
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, 1), plus_hc=use_plus_hc)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (1, 0), JW, plus_hc=use_plus_hc)
if not use_plus_hc:
M.add_coupling(0.25, 0, 'Cd', 0, 'C', (0, -1), JW)
M.add_coupling(1.5, 0, 'Cd', 0, 'C', (-1, 0), JW)
# multi_coupling with a full unit cell inbetween the operators!
M.add_multi_coupling(4., [('N', (0, 0), 0), ('N', (-2, -1), 0)])
# some weird mediated hopping along the diagonal
M.add_multi_coupling(1.125, [('N', (0, 0), 0), ('Cd', (0, 1), 0),
('C', (1, 0), 0)])
H_mpo = M.calc_H_MPO()
W0_new = H_mpo.get_W(0)
W1_new = H_mpo.get_W(1)
Id, JW, N = fermion_site.Id, fermion_site.JW, fermion_site.N
Cd, C = fermion_site.Cd, fermion_site.C
CdJW = Cd.matvec(JW) # = Cd
JWC = JW.matvec(C) # = C
NJW = N.matvec(JW)
# yapf: disable
H_MPO_graph = tenpy.networks.mpo.MPOGraph.from_terms((M.all_onsite_terms(),
M.all_coupling_terms(),
M.exp_decaying_terms),
M.lat.mps_sites(),
M.lat.bc_MPS)
H_MPO_graph._set_ordered_states()
from pprint import pprint
pprint(H_MPO_graph._ordered_states)
pprint(H_MPO_graph._build_grids())
print(M.all_coupling_terms().to_TermList())
# 0.50000 * Cd JW_0 C_1 +
# 1.50000 * Cd JW_0 C_2 +
# 0.50000 * JW C_0 Cd_1 +
# 1.50000 * JW C_0 Cd_2 +
# 1.50000 * Cd JW_1 C_3 +
# 1.50000 * JW C_1 Cd_3 +
# 4.00000 * N_0 N_5 +
# 4.00000 * N_1 N_4 +
# 1.12500 * N_0 Cd JW_1 C_2 +
# 1.12500 * Cd JW_0 N JW_1 C_3
W0_ex = [[Id, CdJW, JWC, N, None, None, None, None, None, N*0.125],
[None, None, None, None, None, Id, None, None, None, None],
[None, None, None, None, None, None, JW*1.5, None, None, None],
[None, None, None, None, None, None, None, JW*1.5, None, None],
[None, None, None, None, Id, None, None, None, None, None],
[None, None, None, None, None, None, JW*1.125, None, None, None],
[None, None, None, None, None, None, None, None, None, C],
[None, None, None, None, None, None, None, None, None, Cd],
[None, None, None, None, None, None, None, None, None, N],
[None, None, None, None, None, None, None, None, Id, None],
[None, None, None, None, None, None, None, None, None, Id]]
W1_ex = [[Id, None, CdJW, JWC, N, None, None, None, None, None, N*0.125],
[None, None, None, None, None, NJW, JW*1.5, None, None, None, C*0.5],
[None, None, None, None, None, None, None, JW*1.5, None, None, Cd*0.5],
[None, Id, None, None, None, None, CdJW*1.125, None, None, None, None],
[None, None, None, None, None, None, None, None, Id*4., None, None],
[None, None, None, None, None, None, None, None, None, Id*4., None],
[None, None, None, None, None, None, None, None, None, None, C],
[None, None, None, None, None, None, None, None, None, None, Cd],
[None, None, None, None, None, None, None, None, None, None, N],
[None, None, None, None, None, None, None, None, None, None, Id]]
# yapf: enable
W0_ex = npc.grid_outer(W0_ex, W0_new.legs[:2])
assert npc.norm(W0_new -
W0_ex) == 0. # coupling constants: no rounding errors
W1_ex = npc.grid_outer(W1_ex, W1_new.legs[:2])
assert npc.norm(W1_new -
W1_ex) == 0. # coupling constants: no rounding errors