def test_MPO_hermitian():
s = spin_half
ot = OnsiteTerms(4)
ct = CouplingTerms(4)
ct.add_coupling_term(1., 2, 3, 'Sm', 'Sp')
H = mpo.MPOGraph.from_terms(ot, ct, [s] * 4, 'infinite').build_MPO()
# assert not H.is_hermitian()
ct.add_coupling_term(1., 2, 3, 'Sp', 'Sm')
H = mpo.MPOGraph.from_terms(ot, ct, [s] * 4, 'infinite').build_MPO()
# assert H.is_hermitian()
ct.add_coupling_term(1., 3, 18, 'Sm', 'Sp')
H = mpo.MPOGraph.from_terms(ot, ct, [s] * 4, 'infinite').build_MPO()
assert not H.is_hermitian()
ct.add_coupling_term(1., 3, 18, 'Sp', 'Sm')
H = mpo.MPOGraph.from_terms(ot, ct, [s] * 4, 'infinite').build_MPO()
assert H.is_hermitian()
def test_MPO_expectation_value():
s = spin_half
psi1 = mps.MPS.from_singlets(s, 6, [(1, 3), (2, 5)], lonely=[0, 4], bc='infinite')
psi1.test_sanity()
ot = OnsiteTerms(4)
ot.add_onsite_term(0.1, 0, 'Sz') # -> 0.5
ot.add_onsite_term(0.2, 3, 'Sz') # -> 0.
ct = CouplingTerms(4) # note: ct.L != psi1.L
ct.add_coupling_term(1., 2, 3, 'Sz', 'Sz') # -> 0.
ct.add_coupling_term(1.5, 1, 3, 'Sz', 'Sz') # -> 1.5*(-0.25)
ct.add_coupling_term(2.5, 0, 6, 'Sz', 'Sz') # -> 2.5*0.25
H = mpo.MPOGraph.from_terms(ot, ct, [s] * 4, 'infinite').build_MPO()
ev = H.expectation_value(psi1)
desired_ev = (0.1 * 0.5 + 0.2 * 0. + 1. * 0. + 1.5 * -0.25 + 2.5 * 0.25) / H.L
assert abs(ev - desired_ev) < 1.e-8
grid = [[s.Id, s.Sz, 3 * s.Sz], [None, 0.1 * s.Id, s.Sz], [None, None, s.Id]]
L = 1
exp_dec_H = mpo.MPO.from_grids([s] * L, [grid] * L, bc='infinite', IdL=0, IdR=2)
ev = exp_dec_H.expectation_value(psi1)
desired_ev = 3 * 0.5 + 0.25 * 0.1**(4 - 1) + 0.25 * 0.1**(6 - 1) + 0.25 * 0.1**(
10 - 1) # values > 1.e-15
assert abs(ev - desired_ev) < 1.e-15
L = 3
exp_dec_H = mpo.MPO.from_grids([s] * L, [grid] * L, bc='infinite', IdL=0, IdR=2)
ev = exp_dec_H.expectation_value(psi1)
desired_ev = (
desired_ev + # first site
3 * 0. - 0.25 * 0.1**(3 - 1 - 1) + # second site
3 * 0. - 0.25 * 0.1**(5 - 2 - 1)) / 3.
print("ev = ", ev, "desired", desired_ev)
assert abs(ev - desired_ev) < 1.e-14
def test_coupling_terms():
L = 4
sites = []
for i in range(L):
s = site.Site(spin_half.leg)
s.add_op("X_{i:d}".format(i=i), 2. * np.eye(2))
s.add_op("Y_{i:d}".format(i=i), 3. * np.eye(2))
sites.append(s)
strength1 = np.arange(0., 5)[:, np.newaxis] + np.arange(
0., 0.625, 0.125)[np.newaxis, :]
c1 = CouplingTerms(L)
for i, j in [(2, 3)]:
c1.add_coupling_term(strength1[i, j], i, j, "X_{i:d}".format(i=i),
"Y_{j:d}".format(j=j))
assert c1.max_range() == 3 - 2
for i, j in [(0, 1), (0, 3), (0, 2)]:
c1.add_coupling_term(strength1[i, j], i, j, "X_{i:d}".format(i=i),
"Y_{j:d}".format(j=j))
c1_des = {0: {('X_0', 'Id'): {1: {'Y_1': 0.125},
2: {'Y_2': 0.25},
3: {'Y_3': 0.375}}},
2: {('X_2', 'Id'): {3: {'Y_3': 2.375}}}} # yapf: disable
assert c1.coupling_terms == c1_des
c1._test_terms(sites)
assert c1.max_range() == 3 - 0
tl1 = c1.to_TermList()
term_list_des = [[('X_0', 0), ('Y_1', 1)], [('X_0', 0), ('Y_2', 2)],
[('X_0', 0), ('Y_3', 3)], [('X_2', 2), ('Y_3', 3)]]
assert tl1.terms == term_list_des
assert np.all(tl1.strength == [0.125, 0.25, 0.375, 2.375])
ot1, ct1_conv = tl1.to_OnsiteTerms_CouplingTerms(sites)
assert ot1.onsite_terms == [{}] * L
assert ct1_conv.coupling_terms == c1_des
mc = MultiCouplingTerms(L)
for i, j in [(2, 3)]: # exact same terms as c1
mc.add_coupling_term(strength1[i, j], i, j, "X_{i:d}".format(i=i),
"Y_{j:d}".format(j=j))
assert mc.max_range() == 3 - 2
for i, j in [(0, 1), (0, 3), (0, 2)]: # exact same terms as c1
mc.add_coupling_term(strength1[i, j], i, j, "X_{i:d}".format(i=i),
"Y_{j:d}".format(j=j))
assert mc.coupling_terms == c1_des
assert mc.max_range() == 3 - 0
mc.add_multi_coupling_term(20., [0, 1, 3], ['X_0', 'Y_1', 'Y_3'],
['Id', 'Id'])
mc.add_multi_coupling_term(30., [0, 1, 3], ['X_0', 'Y_1', 'Y_3'],
['S1', 'S2'])
mc.add_multi_coupling_term(40., [1, 2, 3], ['X_1', 'Y_2', 'Y_3'],
['Id', 'Id'])
mc_des = {0: {('X_0', 'Id'): {1: {'Y_1': 0.125,
('Y_1', 'Id'): {3: {'Y_3': 20.0}}},
2: {'Y_2': 0.25},
3: {'Y_3': 0.375}},
('X_0', 'S1'): {1: {('Y_1', 'S2'): {3: {'Y_3': 30.0}}}}},
1: {('X_1', 'Id'): {2: {('Y_2', 'Id'): {3: {'Y_3': 40.0}}}}},
2: {('X_2', 'Id'): {3: {'Y_3': 2.375}}}} # yapf: disable
assert mc.coupling_terms == mc_des
mc._test_terms(sites)
# convert to TermList
tl_mc = mc.to_TermList()
term_list_des = [
[('X_0', 0), ('Y_1', 1)],
[('X_0', 0), ('Y_1', 1), ('Y_3', 3)],
[('X_0', 0), ('Y_2', 2)],
[('X_0', 0), ('Y_3', 3)],
[('X_0', 0), ('Y_1', 1), ('Y_3', 3)], # (!) droppend S1, S2 (!)
[('X_1', 1), ('Y_2', 2), ('Y_3', 3)],
[('X_2', 2), ('Y_3', 3)]
]
assert tl_mc.terms == term_list_des
assert np.all(tl_mc.strength == [0.125, 20., 0.25, 0.375, 30., 40., 2.375])
ot, mc_conv = tl_mc.to_OnsiteTerms_CouplingTerms(sites)
assert ot1.onsite_terms == [{}] * L
del (mc_des[0])[('X_0', 'S1')] # conversion dropped the opstring names
mc_des[0][('X_0',
'Id')][1][('Y_1',
'Id')][3]['Y_3'] += 30. # add it to other term
assert mc_conv.coupling_terms == mc_des
# addition
c2 = CouplingTerms(L)
for i, j in [(0, 1), (1, 2)]:
c1.add_coupling_term(strength1[i, j], i, j, "X_{i:d}".format(i=i),
"Y_{j:d}".format(j=j))
c1 += c2
c1_des = {0: {('X_0', 'Id'): {1: {'Y_1': 0.25},
2: {'Y_2': 0.25},
3: {'Y_3': 0.375}}},
1: {('X_1', 'Id'): {2: {'Y_2': 1.25}}},
2: {('X_2', 'Id'): {3: {'Y_3': 2.375}}}} # yapf: disable
assert c1.coupling_terms == c1_des
c1._test_terms(sites)
mc += c1
mc_des = {0: {('X_0', 'Id'): {1: {'Y_1': 0.375,
('Y_1', 'Id'): {3: {'Y_3': 20.0}}},
2: {'Y_2': 0.5},
3: {'Y_3': 0.75}},
('X_0', 'S1'): {1: {('Y_1', 'S2'): {3: {'Y_3': 30.0}}}}},
1: {('X_1', 'Id'): {2: {'Y_2': 1.25,
('Y_2', 'Id'): {3: {'Y_3': 40.0}}}}},
2: {('X_2', 'Id'): {3: {'Y_3': 4.75}}}} # yapf: disable
assert mc.coupling_terms == mc_des
# coupling accross mps boundary
mc.add_multi_coupling_term(50., [1, 3, 5], ['X_1', 'Y_3', 'Y_1'],
['STR', 'JW'])
assert mc.max_range() == 5 - 1
mc._test_terms(sites)
# remove the last coupling again
mc.add_multi_coupling_term(-50., [1, 3, 5], ['X_1', 'Y_3', 'Y_1'],
['STR', 'JW'])
mc.remove_zeros()
assert mc.coupling_terms == mc_des
assert mc.max_range() == 3 - 0
def test_MPO_expectation_value(tol=1.e-15):
s = spin_half
psi1 = mps.MPS.from_singlets(s,
6, [(1, 3), (2, 5)],
lonely=[0, 4],
bc='infinite')
psi1.test_sanity()
ot = OnsiteTerms(4) # H.L != psi.L, consider L = lcm(4, 6) = 12
ot.add_onsite_term(0.1, 0, 'Sz') # -> 0.5 * 2 (sites 0, 4, not 8)
ot.add_onsite_term(0.2, 3, 'Sz') # -> 0. (not sites 4, 7, 11)
ct = CouplingTerms(4) # note: ct.L != psi1.L
ct.add_coupling_term(1., 2, 3, 'Sz', 'Sz') # -> 0. (not 2-3, 6-7, 10-11)
ct.add_coupling_term(1.5, 1, 3, 'Sz',
'Sz') # -> 1.5*(-0.25) (1-3, not 5-7, not 9-11)
ct.add_coupling_term(2.5, 0, 6, 'Sz',
'Sz') # -> 2.5*0.25*3 (0-6, 4-10, not 8-14)
H = mpo.MPOGraph.from_terms((ot, ct), [s] * 4, 'infinite').build_MPO()
desired_ev = (0.1 * 0.5 * 2 + 0.2 * 0. + 1. * 0. + 1.5 * -0.25 +
2.5 * 0.25 * 2) / 12
ev_power = H.expectation_value_power(psi1, tol=tol)
assert abs(ev_power - desired_ev) < tol
ev_TM = H.expectation_value_TM(psi1, tol=tol)
assert abs(ev_TM - desired_ev) < tol
ev = H.expectation_value(psi1, tol)
assert abs(ev - desired_ev) < tol
# now with exponentially decaying term
grid = [
[s.Id, s.Sz, 3 * s.Sz],
[None, 0.1 * s.Id, s.Sz],
[None, None, s.Id],
]
L = 1
exp_dec_H = mpo.MPO.from_grids([s] * L, [grid] * L,
bc='infinite',
IdL=0,
IdR=2)
desired_ev = (
3 * 0.5 * 2 + # Sz onsite
0.25 * (
0.1**3 + 0.1**5 + 0.1**9 + 0.1**11 + 0.1**15 + # Z_0 Z_i
0.1**1 + 0.1**5 + 0.1**7 + 0.1**11 + 0.1**13) + # Z_4 Z_i
-0.25 * (
0.1**1 + # Z_1 Z_3
0.1**2) # Z_2 Z_4
+ 0. # other sites
) / 6. # values > 1.e-15
ev_power = exp_dec_H.expectation_value_power(psi1, tol=tol)
ev_TM = exp_dec_H.expectation_value_TM(psi1, tol=tol)
assert abs(ev_power - desired_ev) < tol
assert abs(ev_TM - desired_ev) < tol
ev = exp_dec_H.expectation_value(psi1, tol=tol)
assert abs(ev - desired_ev) < tol
L = 3 # should give exactly the same answer!
exp_dec_H = mpo.MPO.from_grids([s] * L, [grid] * L,
bc='infinite',
IdL=0,
IdR=2)
ev_power = exp_dec_H.expectation_value_power(psi1, tol=tol)
ev_TM = exp_dec_H.expectation_value_TM(psi1, tol=tol)
assert abs(ev_power - desired_ev) < tol
assert abs(ev_TM - desired_ev) < tol
ev = exp_dec_H.expectation_value(psi1, tol=tol)
assert abs(ev - desired_ev) < tol
def test_MPO_addition():
for bc in ['infinite', 'finite']:
print('bc = ', bc, '-' * 40)
s = spin_half
ot1 = OnsiteTerms(4)
ct1 = CouplingTerms(4)
ct1.add_coupling_term(2., 2, 3, 'Sm', 'Sp')
ct1.add_coupling_term(2., 2, 3, 'Sp', 'Sm')
ct1.add_coupling_term(2., 1, 2, 'Sz', 'Sz')
ot1.add_onsite_term(3., 1, 'Sz')
H1 = mpo.MPOGraph.from_terms((ot1, ct1), [s] * 4, bc).build_MPO()
ot2 = OnsiteTerms(4)
ct2 = CouplingTerms(4)
ct2.add_coupling_term(4., 0, 2, 'Sz', 'Sz')
ct2.add_coupling_term(4., 1, 2, 'Sz', 'Sz')
ot2.add_onsite_term(5., 1, 'Sz')
H2 = mpo.MPOGraph.from_terms((ot2, ct2), [s] * 4, bc).build_MPO()
H12_sum = H1 + H2
ot12 = OnsiteTerms(4)
ot12 += ot1
ot12 += ot2
ct12 = CouplingTerms(4)
ct12 += ct1
ct12 += ct2
H12 = mpo.MPOGraph.from_terms((ot12, ct12), [s] * 4, bc).build_MPO()
assert H12.is_equal(H12_sum)