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)
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_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_onsite_terms():
L = 6
strength1 = np.arange(1., 1. + L * 0.25, 0.25)
o1 = OnsiteTerms(L)
for i in [1, 0, 3]:
o1.add_onsite_term(strength1[i], i, "X_{i:d}".format(i=i))
assert o1.onsite_terms == [{"X_0": strength1[0]},
{"X_1": strength1[1]},
{},
{"X_3": strength1[3]},
{},
{}] # yapf: disable
strength2 = np.arange(2., 2. + L * 0.25, 0.25)
o2 = OnsiteTerms(L)
for i in [1, 4, 3, 5]:
o2.add_onsite_term(strength2[i], i, "Y_{i:d}".format(i=i))
o2.add_onsite_term(strength2[3], 3, "X_3") # add to previous part
o2.add_onsite_term(-strength1[1], 1, "X_1") # remove previous part
o1 += o2
assert o1.onsite_terms == [{"X_0": strength1[0]},
{"X_1": 0., "Y_1": strength2[1]},
{},
{"X_3": strength1[3] + strength2[3], "Y_3": strength2[3]},
{"Y_4": strength2[4]},
{"Y_5": strength2[5]}] # yapf: disable
o1.remove_zeros()
assert o1.onsite_terms == [{"X_0": strength1[0]},
{"Y_1": strength2[1]},
{},
{"X_3": strength1[3]+ strength2[3], "Y_3": strength2[3]},
{"Y_4": strength2[4]},
{"Y_5": strength2[5]}] # yapf: disable
# convert to term_list
tl = o1.to_TermList()
assert tl.terms == [[("X_0", 0)], [("Y_1", 1)], [("X_3", 3)], [("Y_3", 3)],
[("Y_4", 4)], [("Y_5", 5)]]
o3, c3 = tl.to_OnsiteTerms_CouplingTerms([None] * L)
assert o3.onsite_terms == o1.onsite_terms
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
