def test_multi_sites_combine_charges():
spin = site.SpinSite(0.5, 'Sz')
spin1 = site.SpinSite(1, 'Sz')
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
spin_ops = {
op_name: get_site_op_flat(spin, op_name)
for op_name in spin.opnames
}
spin1_ops = {
op_name: get_site_op_flat(spin1, op_name)
for op_name in spin1.opnames
}
ferm_ops = {
op_name: get_site_op_flat(ferm, op_name)
for op_name in ferm.opnames
}
site.multi_sites_combine_charges([spin, ferm])
assert tuple(spin.leg.chinfo.names) == ('2*Sz', 'N', 'Sz')
spin.test_sanity()
ferm.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
spin = site.SpinSite(0.5, 'Sz')
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
site.multi_sites_combine_charges([ferm, spin],
same_charges=[[(0, 'Sz'), (1, '2*Sz')]])
assert tuple(ferm.leg.chinfo.names) == ('N', 'Sz')
spin.test_sanity()
ferm.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
# and finally a few more, changing orders as well
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
spin = site.SpinSite(0.5, 'Sz')
spin1 = site.SpinSite(1, 'Sz')
site.multi_sites_combine_charges([ferm, spin1, spin],
same_charges=[[(0, 'Sz'), (2, '2*Sz')]])
assert tuple(ferm.leg.chinfo.names) == ('N', 'Sz', '2*Sz')
spin.test_sanity()
ferm.test_sanity()
spin1.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in spin1_ops.items():
op_flat2 = get_site_op_flat(spin1, op_name)
npt.assert_equal(op_flat, op_flat2)
def test_spin_half_fermion_site():
for cons_N, cons_Sz in it.product(['N', 'parity', None], ['Sz', 'parity', None]):
print("conserve ", repr(cons_N), repr(cons_Sz))
S = site.SpinHalfFermionSite(cons_N, cons_Sz)
S.test_sanity()
Id = S.Id.to_ndarray()
JW = S.JW.to_ndarray()
Cu, Cd = S.Cu.to_ndarray(), S.Cd.to_ndarray()
Cdu, Cdd = S.Cdu.to_ndarray(), S.Cdd.to_ndarray()
Nu, Nd, Ntot = S.Nu.to_ndarray(), S.Nd.to_ndarray(), S.Ntot.to_ndarray()
npt.assert_equal(np.dot(Cdu, Cu), Nu)
npt.assert_equal(np.dot(Cdd, Cd), Nd)
npt.assert_equal(Nu + Nd, Ntot)
npt.assert_equal(np.dot(Nu, Nd), S.NuNd.to_ndarray())
npt.assert_equal(anticommutator(Cdu, Cu), Id)
npt.assert_equal(anticommutator(Cdd, Cd), Id)
# anti-commutate with Jordan-Wigner
npt.assert_equal(np.dot(Cu, JW), -np.dot(JW, Cu))
npt.assert_equal(np.dot(Cd, JW), -np.dot(JW, Cd))
npt.assert_equal(np.dot(Cdu, JW), -np.dot(JW, Cdu))
npt.assert_equal(np.dot(Cdd, JW), -np.dot(JW, Cdd))
# anti-commute Cu with Cd
npt.assert_equal(np.dot(Cu, Cd), -np.dot(Cd, Cu))
npt.assert_equal(np.dot(Cu, Cdd), -np.dot(Cdd, Cu))
npt.assert_equal(np.dot(Cdu, Cd), -np.dot(Cd, Cdu))
npt.assert_equal(np.dot(Cdu, Cdd), -np.dot(Cdd, Cdu))
if cons_Sz != 'Sz':
SxSy = ['Sx', 'Sy']
else:
SxSy = None
check_spin_site(S, SxSy=SxSy)
def test_expectation_value_term():
s = spin_half
psi1 = mps.MPS.from_singlets(s, 6, [(1, 3), (2, 5)], lonely=[0, 4], bc='finite')
ev = psi1.expectation_value_term([('Sz', 2), ('Sz', 3)])
assert abs(0. - ev) < 1.e-14
ev = psi1.expectation_value_term([('Sz', 1), ('Sz', 3)])
assert abs(-0.25 - ev) < 1.e-14
ev = psi1.expectation_value_term([('Sz', 3), ('Sz', 1), ('Sz', 4)])
assert abs(-0.25 * 0.5 - ev) < 1.e-14
fs = site.SpinHalfFermionSite()
# check fermionic signs
psi2 = mps.MPS.from_product_state([fs] * 4, ['empty', 'up', 'down', 'full'], bc="infinite")
ev = psi2.expectation_value_term([('Cu', 2), ('Nu', 1), ('Cdu', 2)])
assert 1. == ev
ev2 = psi2.expectation_value_term([('Cu', 2), ('Cd', 1), ('Cdd', 1), ('Cdu', 2)])
assert ev2 == ev
ev3 = psi2.expectation_value_term([('Cd', 1), ('Cu', 2), ('Cdd', 1), ('Cdu', 2)])
assert ev3 == -ev2
# over the infinite MPS boundary
ev = psi2.expectation_value_term([('Nu', 1), ('Nd', 4)]) # should be zero
assert abs(ev) == 0.
ev = psi2.expectation_value_term([('Nu', 1), ('Nd', 6)])
assert abs(ev) == 1.
# terms_sum
pref = np.random.random([5])
term_list = TermList(
[[('Nd', 0)], [('Nu', 1), ('Nd', 2)], [('Nd', 2),
('Nu', 5)], [('Nu Nd', 3)], [('Nu', 1),
('Nu', 5)]], pref)
desired = sum(pref[1:])
assert desired == sum(
[psi2.expectation_value_term(term) * strength for term, strength in term_list])
evsum, _ = psi2.expectation_value_terms_sum(term_list)
assert abs(evsum - desired) < 1.e-14
def test_spin_half_fermion_site_ops():
sites = []
for cons_n, cons_sz in it.product(['N', 'parity', None],
['Sz', 'parity', None]):
S = site.SpinHalfFermionSite(cons_n, cons_sz)
sites.append(S)
check_same_operators(sites)
def test_correlation_function():
s = spin_half
psi1 = mps.MPS.from_singlets(s, 6, [(1, 3), (2, 5)], lonely=[0, 4], bc='finite')
corr1 = psi1.correlation_function('Sz', 'Sz')
corr1_exact = 0.25 * np.array([[ 1., 0., 0., 0., 1., 0.],
[ 0., 1., 0., -1., 0., 0.],
[ 0., 0., 1., 0., 0., -1.],
[ 0., -1., 0., 1., 0., 0.],
[ 1., 0., 0., 0., 1., 0.],
[ 0., 0., -1., 0., 0., 1.]]) # yapf: disable
npt.assert_almost_equal(corr1, corr1_exact)
corr1 = psi1.term_correlation_function_right([('Sz', 0)], [('Sz', 0)])
npt.assert_almost_equal(corr1, corr1_exact[0, 1:])
corr1 = psi1.term_correlation_function_right([('Sz', 0)], [('Sz', 1)])
npt.assert_almost_equal(corr1, corr1_exact[0, 1:])
corr1 = psi1.term_correlation_function_right([('Sz', 1)], [('Sz', 1)])
npt.assert_almost_equal(corr1, corr1_exact[1, 2:])
corr1 = psi1.term_correlation_function_right([('Sz', 1)], [('Sz', -1)])
npt.assert_almost_equal(corr1, corr1_exact[1, 2:-1])
corr1 = psi1.term_correlation_function_left([('Sz', 0)], [('Sz', 0)], range(0, 5), 5)
npt.assert_almost_equal(corr1[::-1], corr1_exact[:-1, 5])
corr1 = psi1.term_correlation_function_left([('Sz', 1)], [('Sz', 1)], range(0, 4), 4)
npt.assert_almost_equal(corr1[::-1], corr1_exact[1:-1, 5])
# check fermionic signs
fs = site.SpinHalfFermionSite()
psi2 = mps.MPS.from_product_state([fs] * 4, ['empty', 'up', 'down', 'full'], bc="infinite")
corr2 = psi2.correlation_function('Cdu', 'Cu')
corr2_exact = np.array([[ 0., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 1.]]) # yapf: disable
npt.assert_almost_equal(corr2, corr2_exact)
psi3 = psi2.copy()
from tenpy.algorithms.tebd import RandomUnitaryEvolution
RandomUnitaryEvolution(psi3, {'N_steps': 4}).run()
corr3 = psi3.correlation_function('Cdu', 'Cu')
corr3_d = psi3.correlation_function('Cu', 'Cdu')
npt.assert_almost_equal(np.diag(corr3) + np.diag(corr3_d), 1.)
corr3 = corr3 - np.diag(np.diag(corr3)) # remove diagonal
corr3_d = corr3_d - np.diag(np.diag(corr3_d))
npt.assert_array_almost_equal(corr3, -corr3_d.T) # check anti-commutation of operators
corr = psi3.term_correlation_function_right([('Cdu', 0)], [('Cu', 0)], j_R=range(1, 4))
npt.assert_almost_equal(corr, corr3[0, 1:])
corr3_long = psi3.correlation_function('Cdu', 'Cu', [0], range(4, 11 * 4, 4)).flatten()
corr3_long2 = psi3.term_correlation_function_right([('Cdu', 0)], [('Cu', 0)])
npt.assert_array_almost_equal(corr3_long, corr3_long2)
def test_spin_half_fermion_site():
hcs = dict(Id='Id', JW='JW', JWu='JWu', JWd='JWd',
Cu='Cdu', Cdu='Cu', Cd='Cdd', Cdd='Cd',
Nu='Nu', Nd='Nd', NuNd='NuNd', Ntot='Ntot', dN='dN',
Sx='Sx', Sy='Sy', Sz='Sz', Sp='Sm', Sm='Sp') # yapf: disable
sites = []
for cons_N, cons_Sz in it.product(['N', 'parity', None],
['Sz', 'parity', None]):
print("conserve ", repr(cons_N), repr(cons_Sz))
S = site.SpinHalfFermionSite(cons_N, cons_Sz)
S.test_sanity()
for op in S.onsite_ops:
assert S.hc_ops[op] == hcs[op]
Id = S.Id.to_ndarray()
JW = S.JW.to_ndarray()
Cu, Cd = S.Cu.to_ndarray(), S.Cd.to_ndarray()
Cdu, Cdd = S.Cdu.to_ndarray(), S.Cdd.to_ndarray()
Nu, Nd, Ntot = S.Nu.to_ndarray(), S.Nd.to_ndarray(), S.Ntot.to_ndarray(
)
npt.assert_equal(np.dot(Cdu, Cu), Nu)
npt.assert_equal(np.dot(Cdd, Cd), Nd)
npt.assert_equal(Nu + Nd, Ntot)
npt.assert_equal(np.dot(Nu, Nd), S.NuNd.to_ndarray())
npt.assert_equal(anticommutator(Cdu, Cu), Id)
npt.assert_equal(anticommutator(Cdd, Cd), Id)
# anti-commutate with Jordan-Wigner
npt.assert_equal(np.dot(Cu, JW), -np.dot(JW, Cu))
npt.assert_equal(np.dot(Cd, JW), -np.dot(JW, Cd))
npt.assert_equal(np.dot(Cdu, JW), -np.dot(JW, Cdu))
npt.assert_equal(np.dot(Cdd, JW), -np.dot(JW, Cdd))
# anti-commute Cu with Cd
npt.assert_equal(np.dot(Cu, Cd), -np.dot(Cd, Cu))
npt.assert_equal(np.dot(Cu, Cdd), -np.dot(Cdd, Cu))
npt.assert_equal(np.dot(Cdu, Cd), -np.dot(Cd, Cdu))
npt.assert_equal(np.dot(Cdu, Cdd), -np.dot(Cdd, Cdu))
if cons_Sz != 'Sz':
SxSy = ['Sx', 'Sy']
else:
SxSy = None
check_spin_site(S, SxSy=SxSy)
sites.append(S)
check_same_operators(sites)
def test_correlation_function():
s = spin_half
Pup = s.Id.copy()
Pup[s.state_labels['down'], s.state_labels['down']] = 0.
Pdown = s.Id.copy()
Pdown[s.state_labels['up'], s.state_labels['up']] = 0.
s.add_op('Pup', Pup, need_JW=False, hc='Pup')
s.add_op('Pdown', Pdown, need_JW=False, hc='Pdown')
psi1 = mps.MPS.from_singlets(s,
6, [(1, 3), (2, 5)],
lonely=[0, 4],
bc='finite')
corr1 = psi1.correlation_function('Sz', 'Sz')
corr1_exact = 0.25 * np.array([[ 1., 0., 0., 0., 1., 0.],
[ 0., 1., 0., -1., 0., 0.],
[ 0., 0., 1., 0., 0., -1.],
[ 0., -1., 0., 1., 0., 0.],
[ 1., 0., 0., 0., 1., 0.],
[ 0., 0., -1., 0., 0., 1.]]) # yapf: disable
npt.assert_almost_equal(corr1, corr1_exact)
corr1 = psi1.term_correlation_function_right([('Sz', 0)], [('Sz', 0)])
npt.assert_almost_equal(corr1, corr1_exact[0, 1:])
corr1 = psi1.term_correlation_function_right([('Sz', 0)], [('Sz', 1)])
npt.assert_almost_equal(corr1, corr1_exact[0, 1:])
corr1 = psi1.term_correlation_function_right([('Sz', 1)], [('Sz', 1)])
npt.assert_almost_equal(corr1, corr1_exact[1, 2:])
corr1 = psi1.term_correlation_function_right([('Sz', 1)], [('Sz', -1)])
npt.assert_almost_equal(corr1, corr1_exact[1, 2:-1])
corr1 = psi1.term_correlation_function_left([('Sz', 0)], [('Sz', 0)],
range(0, 5), 5)
npt.assert_almost_equal(corr1[::-1], corr1_exact[:-1, 5])
corr1 = psi1.term_correlation_function_left([('Sz', 1)], [('Sz', 1)],
range(0, 4), 4)
npt.assert_almost_equal(corr1[::-1], corr1_exact[1:-1, 5])
Sz = TermList([[('Pup', 0)], [('Pdown', 0)]],
[0.5, -0.5]) # complicated way to write Sz
corr1 = psi1.term_list_correlation_function_right(Sz, Sz)
# check term_list_correlation_function_right for terms with different qtotal
npt.assert_almost_equal(corr1, corr1_exact[0, 1:])
Sx = TermList([[('Sp', 0)], [('Sm', 0)]],
[0.5, +0.5]) # complicated way to write Sx_0
Sy = TermList([[('Sp', 1)], [('Sm', 1)]],
[-0.5j, +0.5j]) # complicated way to write Sy_1
corrxx = psi1.term_list_correlation_function_right(Sx, Sx)
npt.assert_almost_equal(corrxx, np.zeros((5, ))) # Sx_0 gives 0
corrxx = psi1.term_list_correlation_function_right(Sx, Sx, 1)
npt.assert_almost_equal(corrxx, 0.25 * np.array([0., -1., 0., 0.]))
corrxy = psi1.term_list_correlation_function_right(Sx, Sy, 1, range(1, 5))
npt.assert_almost_equal(corrxy, np.zeros((4, )))
# check fermionic signs
fs = site.SpinHalfFermionSite()
psi2 = mps.MPS.from_product_state([fs] * 4,
['empty', 'up', 'down', 'full'],
bc="infinite")
corr2 = psi2.correlation_function('Cdu', 'Cu')
corr2_exact = np.array([[ 0., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 1.]]) # yapf: disable
npt.assert_almost_equal(corr2, corr2_exact)
psi3 = psi2.copy()
from tenpy.algorithms.tebd import RandomUnitaryEvolution
RandomUnitaryEvolution(psi3, {'N_steps': 4}).run()
corr3 = psi3.correlation_function('Cdu', 'Cu')
corr3_d = psi3.correlation_function('Cu', 'Cdu')
npt.assert_almost_equal(np.diag(corr3) + np.diag(corr3_d), 1.)
corr3 = corr3 - np.diag(np.diag(corr3)) # remove diagonal
corr3_d = corr3_d - np.diag(np.diag(corr3_d))
npt.assert_array_almost_equal(
corr3, -corr3_d.T) # check anti-commutation of operators
corr = psi3.term_correlation_function_right([('Cdu', 0)], [('Cu', 0)],
j_R=range(1, 4))
npt.assert_almost_equal(corr, corr3[0, 1:])
corr3_long = psi3.correlation_function('Cdu', 'Cu', [0],
range(4, 11 * 4, 4)).flatten()
corr3_long2 = psi3.term_correlation_function_right([('Cdu', 0)],
[('Cu', 0)])
npt.assert_array_almost_equal(corr3_long, corr3_long2)
term1 = TermList([[('Cdu', 0)]], [1.])
term2 = TermList([[('Cu', 0)], [('Ntot', -1)]],
[1., 2.]) # N shouldn't contribute!
corr3_long3 = psi3.term_list_correlation_function_right(term1, term2)
def test_set_common_charges():
spin = site.SpinSite(0.5, 'Sz')
spin1 = site.SpinSite(1, 'Sz')
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
boson = site.BosonSite(2, 'N')
spin_ops = {
op_name: get_site_op_flat(spin, op_name)
for op_name in spin.opnames
}
spin1_ops = {
op_name: get_site_op_flat(spin1, op_name)
for op_name in spin1.opnames
}
ferm_ops = {
op_name: get_site_op_flat(ferm, op_name)
for op_name in ferm.opnames
}
boson_ops = {
op_name: get_site_op_flat(boson, op_name)
for op_name in boson.opnames
}
site.set_common_charges([spin, ferm])
assert tuple(spin.leg.chinfo.names) == ('2*Sz', 'N')
spin.test_sanity()
ferm.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
spin = site.SpinSite(0.5, 'Sz')
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
site.set_common_charges([ferm, spin],
new_charges=[[(1, 0, '2*Sz'), (1, 1, '2*Sz')]])
assert tuple(ferm.leg.chinfo.names) == ('2*Sz', )
spin.test_sanity()
ferm.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
# and finally a few more, changing orders as well
ferm = site.SpinHalfFermionSite(cons_N='N', cons_Sz='Sz')
spin = site.SpinSite(0.5, 'Sz')
spin1 = site.SpinSite(1, 'Sz')
boson = site.BosonSite(2, 'N')
site.set_common_charges(
[ferm, spin1, spin, boson],
new_charges=[[(1, 0, '2*Sz'), (1, 2, '2*Sz')],
[(2, 0, 'N'), (1, 3, 'N')], [(0.5, 1, '2*Sz')]],
new_names=['2*(Sz_f + Sz_spin-half)', '2*N_f+N_b', 'Sz_spin-1'])
assert tuple(ferm.leg.chinfo.names) == ('2*(Sz_f + Sz_spin-half)',
'2*N_f+N_b', 'Sz_spin-1')
spin.test_sanity()
ferm.test_sanity()
spin1.test_sanity()
boson.test_sanity()
for op_name, op_flat in spin_ops.items():
op_flat2 = get_site_op_flat(spin, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in ferm_ops.items():
op_flat2 = get_site_op_flat(ferm, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in spin1_ops.items():
op_flat2 = get_site_op_flat(spin1, op_name)
npt.assert_equal(op_flat, op_flat2)
for op_name, op_flat in boson_ops.items():
op_flat2 = get_site_op_flat(boson, op_name)
npt.assert_equal(op_flat, op_flat2)
