def test_lattice_order():
s = site.SpinHalfSite('Sz')
# yapf: disable
square = lattice.Square(2, 2, s, order='default')
order_default = np.array([[0, 0, 0], [0, 1, 0], [1, 0, 0], [1, 1, 0]])
npt.assert_equal(square.order, order_default)
square = lattice.Square(4, 3, s, order='snake')
order_snake = np.array([[0, 0, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0], [1, 1, 0], [1, 0, 0],
[2, 0, 0], [2, 1, 0], [2, 2, 0], [3, 2, 0], [3, 1, 0], [3, 0, 0]])
npt.assert_equal(square.order, order_snake)
square = lattice.Square(2, 3, s, order=("standard", (True, False), (1, 0)))
order_Fsnake = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0]])
npt.assert_equal(square.order, order_Fsnake)
hc = lattice.Honeycomb(2, 3, s, order='default')
order_hc_def = np.array([[0, 0, 0], [0, 1, 0], [0, 2, 0], [0, 0, 1], [0, 1, 1], [0, 2, 1],
[1, 0, 0], [1, 1, 0], [1, 2, 0], [1, 0, 1], [1, 1, 1], [1, 2, 1]])
npt.assert_equal(hc.order, order_hc_def)
hc = lattice.Honeycomb(2, 3, s, order=('standard', (True, False, False), (0.3, 0.1, -1.)))
order_hc_mix = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0],
[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1], [0, 2, 1], [1, 2, 1]])
npt.assert_equal(hc.order, order_hc_mix)
kag = lattice.Kagome(2, 3, s, order=('grouped', [[1], [0, 2]]))
order_kag_gr = np.array([[0, 0, 1], [0, 1, 1], [0, 2, 1], [0, 0, 0], [0, 0, 2], [0, 1, 0],
[0, 1, 2], [0, 2, 0], [0, 2, 2],
[1, 0, 1], [1, 1, 1], [1, 2, 1], [1, 0, 0], [1, 0, 2], [1, 1, 0],
[1, 1, 2], [1, 2, 0], [1, 2, 2]])
npt.assert_equal(kag.order, order_kag_gr)
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_number_nn():
s = site.SpinHalfSite('Sz')
chain = lattice.Chain(2, s)
assert chain.number_nearest_neighbors() == 2
assert chain.number_next_nearest_neighbors() == 2
ladd = lattice.Ladder(2, s)
assert ladd.number_nearest_neighbors(0) == 3
assert ladd.number_nearest_neighbors(1) == 3
assert ladd.number_next_nearest_neighbors(0) == 2
assert ladd.number_next_nearest_neighbors(1) == 2
square = lattice.Square(2, 2, s)
assert square.number_nearest_neighbors() == 4
assert square.number_next_nearest_neighbors() == 4
triang = lattice.Triangular(2, 2, s)
assert triang.number_nearest_neighbors() == 6
assert triang.number_next_nearest_neighbors() == 6
hc = lattice.Honeycomb(2, 2, s)
assert hc.number_nearest_neighbors(0) == 3
assert hc.number_nearest_neighbors(1) == 3
assert hc.number_next_nearest_neighbors(0) == 6
assert hc.number_next_nearest_neighbors(1) == 6
kag = lattice.Kagome(2, 2, s)
assert kag.number_nearest_neighbors(0) == 4
assert kag.number_nearest_neighbors(1) == 4
assert kag.number_nearest_neighbors(2) == 4
assert kag.number_next_nearest_neighbors(0) == 4
assert kag.number_next_nearest_neighbors(1) == 4
assert kag.number_next_nearest_neighbors(2) == 4
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_pairs():
lattices = [
lattice.Chain(2, None),
lattice.Ladder(2, None),
lattice.Square(2, 2, None),
lattice.Triangular(2, 2, None),
lattice.Honeycomb(2, 2, None),
lattice.Kagome(2, 2, None)
]
for lat in lattices:
print(lat.__class__.__name__)
found_dist_pairs = lat.find_coupling_pairs(5, 3.)
dists = sorted(found_dist_pairs.keys())
for i, name in enumerate([
'nearest_neighbors', 'next_nearest_neighbors', 'next_next_nearest_neighbors',
'fourth_nearest_neighbors', 'fifth_nearest_neighbors'
]):
if name not in lat.pairs:
assert i > 2 # all of them should define up to next_next_nearest_neighbors
continue
print(name)
defined_pairs = lat.pairs[name]
found_pairs = found_dist_pairs[dists[i]]
assert len(defined_pairs) == len(found_pairs)
defined_pairs = pairs_with_reversed(defined_pairs)
found_pairs = pairs_with_reversed(found_pairs)
assert defined_pairs == found_pairs
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_MultiCouplingModel_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.MultiCouplingModel(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_lattice_order():
s = site.SpinHalfSite('Sz')
# yapf: disable
square = lattice.Square(2, 2, s, 'default')
order_default = np.array([[0, 0, 0], [0, 1, 0], [1, 0, 0], [1, 1, 0]])
npt.assert_equal(square.order, order_default)
square = lattice.Square(4, 3, s, 'snake')
order_snake = np.array([[0, 0, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0], [1, 1, 0], [1, 0, 0],
[2, 0, 0], [2, 1, 0], [2, 2, 0], [3, 2, 0], [3, 1, 0], [3, 0, 0]])
npt.assert_equal(square.order, order_snake)
square = lattice.Square(2, 3, s, ((1, 0), (True, False)))
order_Fsnake = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0]])
npt.assert_equal(square.order, order_Fsnake)
hc = lattice.Honeycomb(2, 3, s, s, 'default')
order_hc_def = np.array([[0, 0, 0], [0, 1, 0], [0, 2, 0], [0, 0, 1], [0, 1, 1], [0, 2, 1],
[1, 0, 0], [1, 1, 0], [1, 2, 0], [1, 0, 1], [1, 1, 1], [1, 2, 1]])
npt.assert_equal(hc.order, order_hc_def)
hc = lattice.Honeycomb(2, 3, s, s, ((0.3, 0.1, -1.), (True, False, False)))
order_hc_mix = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 2, 0], [1, 2, 0],
[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1], [0, 2, 1], [1, 2, 1]])
npt.assert_equal(hc.order, order_hc_mix)
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_number_nn():
s = site.SpinHalfSite('Sz')
chain = lattice.Chain(2, s)
assert chain.number_nearest_neighbors() == 2
assert chain.number_next_nearest_neighbors() == 2
square = lattice.Square(2, 2, s)
print(square.number_next_nearest_neighbors())
assert square.number_nearest_neighbors() == 4
assert square.number_next_nearest_neighbors() == 4
hc = lattice.Honeycomb(2, 2, s, s)
assert hc.number_nearest_neighbors(0) == 3
assert hc.number_nearest_neighbors(1) == 3
assert hc.number_next_nearest_neighbors(0) == 6
assert hc.number_next_nearest_neighbors(1) == 6
def plot_bc_shift_comparison(name="square_bc_shift"):
print(name)
Lx, Ly = 4, 3
fig, axes = plt.subplots(1, 3, True, True, figsize=(5, 2))
for shift, ax in zip([1, 0, -1], axes):
lat = lattice.Square(Lx, Ly, None, bc=['periodic', shift])
lat.plot_sites(ax)
lat.plot_coupling(ax)
lat.plot_basis(ax, color='g', linewidth=2.)
lat.plot_bc_identified(ax)
ax.set_title("shift = " + str(shift))
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
axes[0].set_aspect('equal')
plt.savefig(name + ".png")
plt.savefig(name + ".pdf")
def test_number_nn():
s = site.SpinHalfSite('Sz')
chain = lattice.Chain(2, s)
assert chain.count_neighbors() == 2
assert chain.count_neighbors(key='next_nearest_neighbors') == 2
ladd = lattice.Ladder(2, s)
for u in [0, 1]:
assert ladd.count_neighbors(u) == 3
assert ladd.count_neighbors(u, key='next_nearest_neighbors') == 2
square = lattice.Square(2, 2, s)
assert square.count_neighbors() == 4
assert square.count_neighbors(key='next_nearest_neighbors') == 4
triang = lattice.Triangular(2, 2, s)
assert triang.count_neighbors() == 6
assert triang.count_neighbors(key='next_nearest_neighbors') == 6
hc = lattice.Honeycomb(2, 2, s)
for u in [0, 1]:
assert hc.count_neighbors(u) == 3
assert hc.count_neighbors(u, key='next_nearest_neighbors') == 6
kag = lattice.Kagome(2, 2, s)
for u in [0, 1, 2]:
assert kag.count_neighbors(u) == 4
assert kag.count_neighbors(u, key='next_nearest_neighbors') == 4
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
