def test_CouplingModel():
for bc in ['open', 'periodic']:
M = model.CouplingModel(spin_half_lat, bc)
M.add_coupling(1.2, 0, 'Sz', 0, 'Sz', 1)
M.test_sanity()
M = model.CouplingModel(fermion_lat, bc)
M.add_coupling(1.2, 0, 'Cd', 0, 'C', 1, 'JW')
M.test_sanity()
def test_ext_flux():
Lx, Ly = 3, 4
lat = lattice.Square(Lx, Ly, fermion_site, bc=['periodic', 'periodic'], bc_MPS='infinite')
M = model.CouplingModel(lat)
strength = 1.23
strength_array = np.ones((Lx, Ly)) * strength
for phi in [0, 2 * np.pi]: # flux shouldn't do anything
print("phi = ", phi)
for dx in [1, 0], [0, 1], [0, 2], [1, -1], [-2, 2]:
print("dx = ", dx)
strength_flux = M.coupling_strength_add_ext_flux(strength, [1, 0], [0, phi])
npt.assert_array_almost_equal_nulp(strength_flux, strength_array, 10)
for phi in [np.pi / 2, 0.123]:
print("phi = ", phi)
strength_hop_x = M.coupling_strength_add_ext_flux(strength, [1, 0], [0, phi])
npt.assert_array_almost_equal_nulp(strength_hop_x, strength_array, 10)
expect_y_1 = np.array(strength_array, dtype=np.complex128)
expect_y_1[:, -1:] = strength * np.exp(1.j * phi)
for dx in [[0, 1], [0, -1], [1, -1], [1, 1]]:
print("dx = ", dx)
strength_hop_y_1 = M.coupling_strength_add_ext_flux(strength, dx, [0, phi])
if dx[1] < 0:
npt.assert_array_almost_equal_nulp(strength_hop_y_1, expect_y_1, 10)
else:
npt.assert_array_almost_equal_nulp(strength_hop_y_1, np.conj(expect_y_1), 10)
expect_y_2 = np.array(strength_array, dtype=np.complex128)
expect_y_2[:, -2:] = strength * np.exp(1.j * phi)
for dx in [[0, 2], [0, -2], [1, 2], [3, 2]]:
print("dx = ", dx)
strength_hop_y_2 = M.coupling_strength_add_ext_flux(strength, dx, [0, phi])
if dx[1] < 0:
npt.assert_array_almost_equal_nulp(strength_hop_y_2, expect_y_2, 10)
else:
npt.assert_array_almost_equal_nulp(strength_hop_y_2, np.conj(expect_y_2), 10)
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 test_CouplingModel_fermions():
for bc, bc_MPS in zip(['open', 'periodic'], ['finite', 'infinite']):
fermion_lat = lattice.Chain(5, fermion_site, bc=bc, bc_MPS=bc_MPS)
M = model.CouplingModel(fermion_lat)
M.add_coupling(1.2, 0, 'Cd', 0, 'C', 1, 'JW')
M.add_coupling(1.2, 0, 'Cd', 0, 'C', -1, 'JW')
M.test_sanity()
M.calc_H_MPO()
M.calc_H_bond()
def test_CouplingModel():
for bc in ['open', 'periodic']:
spin_half_lat = lattice.Chain(5, spin_half_site, bc=bc, bc_MPS='finite')
M = model.CouplingModel(spin_half_lat)
M.add_coupling(1.2, 0, 'Sz', 0, 'Sz', 1)
M.test_sanity()
M.calc_H_MPO()
if bc == 'periodic':
with pytest.raises(ValueError, match="nearest neighbor"):
M.calc_H_bond() # should raise a ValueError
# periodic bc but finite bc_MPS leads to a long-range coupling
else:
M.calc_H_bond()
def test_CouplingModel():
spin_half_lat = lattice.Chain(5, spin_half_site, bc_MPS='finite')
for bc in ['open', 'periodic']:
M = model.CouplingModel(spin_half_lat, bc)
M.add_coupling(1.2, 0, 'Sz', 0, 'Sz', 1)
M.test_sanity()
M.calc_H_MPO()
if bc == 'periodic':
with nose.tools.assert_raises(ValueError):
M.calc_H_bond() # should raise a ValueError
# periodic bc but finite bc_MPS leads to a long-range coupling
else:
M.calc_H_bond()
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_CouplingModel_shift(Lx=3, Ly=3, shift=1):
bc = ['periodic', shift]
spin_half_square = lattice.Square(Lx,
Ly,
spin_half_site,
bc=bc,
bc_MPS='infinite')
M = model.CouplingModel(spin_half_square)
M.add_coupling(1.2, 0, 'Sz', 0, 'Sz', [1, 0])
M.add_multi_coupling(0.8, [('Sz', [0, 0], 0), ('Sz', [0, 1], 0),
('Sz', [1, 0], 0)])
M.test_sanity()
H = M.calc_H_MPO()
dims = [W.shape[0] for W in H._W]
# check translation invariance of the MPO: at least the dimensions should fit
# (the states are differently ordered, so the matrices differ!)
for i in range(1, Lx):
assert dims[:Lx] == dims[i * Lx:(i + 1) * Lx]
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
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