def test_christoffel(self):
mps = self.mps_0_6.left_canonicalise()
ijks = ((4, 5, 4), (3, 5, 3), (3, 4, 3)) # all non zero indexes (for full rank)
for i, j, k in ijks:
# Gauge projectors are in the right place
mps.left_canonicalise()
l, r = mps.get_envs()
self.assertTrue(not allclose(mps.christoffel(i, j, k), 0))
i_true=allclose(mps.christoffel(i, j, k, closed=(l(i-1)@c(mps[i]), None, None)), 0)
i_false=allclose(mps.christoffel(i, j, k, closed=(l(i-1)@mps[i], None, None)), 0)
j_true=allclose(mps.christoffel(i, j, k, closed=(None, l(j-1)@c(mps[j]), None)), 0)
j_false=allclose(mps.christoffel(i, j, k, closed=(None, l(j-1)@mps[j], None)), 0)
k_true=allclose(mps.christoffel(i, j, k, closed=(None, None, l(k-1)@mps[k])), 0)
k_false=allclose(mps.christoffel(i, j, k, closed=(None, None, l(k-1)@c(mps[k]))), 0)
self.assertTrue(i_true)
self.assertTrue(j_true)
self.assertTrue(k_true)
self.assertTrue(not i_false)
self.assertTrue(not j_false)
self.assertTrue(not k_false)
mps.right_canonicalise()
l, r = mps.get_envs()
self.assertTrue(not allclose(mps.christoffel(i, j, k), 0))
i_true=allclose(mps.christoffel(i, j, k, closed=(l(i-1)@c(mps[i]), None, None)), 0)
i_false=allclose(mps.christoffel(i, j, k, closed=(l(i-1)@mps[i], None, None)), 0)
j_true=allclose(mps.christoffel(i, j, k, closed=(None, l(j-1)@c(mps[j]), None)), 0)
j_false=allclose(mps.christoffel(i, j, k, closed=(None, l(j-1)@mps[j], None)), 0)
k_true=allclose(mps.christoffel(i, j, k, closed=(None, None, l(k-1)@mps[k])), 0)
k_false=allclose(mps.christoffel(i, j, k, closed=(None, None, l(k-1)@c(mps[k]))), 0)
self.assertTrue(i_true)
self.assertTrue(j_true)
self.assertTrue(k_true)
self.assertTrue(not i_false)
self.assertTrue(not j_false)
self.assertTrue(not k_false)
# symmetric in i, j
self.assertTrue(allclose(mps.christoffel(i, j, k, closed=(c(mps[i]), c(mps[j]), mps[k])),
mps.christoffel(j, i, k, closed=(c(mps[j]), c(mps[i]), mps[k])) ))
self.assertTrue(allclose(tra(mps.christoffel(i, j, k), [3, 4, 5, 0, 1, 2, 6, 7, 8]), mps.christoffel(j, i, k)))
ijks = ((1, 2, 1),)
for i, j, k in ijks:
# Christoffel symbols that are zero for untruncated become not zero after truncation
self.assertTrue(allclose(mps.christoffel(i, j, k), 0))
mps.left_canonicalise(2)
self.assertTrue(not allclose(mps.christoffel(i, j, k), 0))
def test_Maps(self):
for tm in self.maps:
r = rand(tm.shape[1])
full_tm = transpose(tensordot(tm.A, C(tm.B), [0, 0]),
[0, 2, 1, 3]).reshape(tm.shape)
self.assertTrue(allclose(full_tm @ r, tm.mv(r)))
self.assertTrue(allclose(c(r @ full_tm), tm.mvr(r)))
def test_Map_operators(self):
for tm in self.maps:
r = rand(tm.shape[1])
full_tm = transpose(tensordot(tm.A, C(tm.B), [0, 0]),
[0, 2, 1, 3]).reshape(tm.shape)
self.assertTrue(allclose(full_tm @ r, tm.aslinearoperator() @ (r)))
self.assertTrue(
allclose(c(r @ full_tm),
tm.aslinearoperator().H @ r))
def test_F2_F1(self):
'''<d_id_j ψ|H|ψ>, <d_iψ|H|d_jψ>'''
Sx1, Sy1, Sz1 = N_body_spins(0.5, 1, 6)
Sx2, Sy2, Sz2 = N_body_spins(0.5, 2, 6)
Sx3, Sy3, Sz3 = N_body_spins(0.5, 3, 6)
Sx4, Sy4, Sz4 = N_body_spins(0.5, 4, 6)
Sx5, Sy5, Sz5 = N_body_spins(0.5, 5, 6)
Sx6, Sy6, Sz6 = N_body_spins(0.5, 6, 6)
Sx12, Sy12, Sz12 = N_body_spins(0.5, 1, 2)
Sx22, Sy22, Sz22 = N_body_spins(0.5, 2, 2)
mps = self.mps_0_6.left_canonicalise()
listH = [Sz12@Sz22+Sx12, Sz12@Sz22+Sx12+Sx22, Sz12@Sz22+Sx22+Sx12+Sx22, Sz12@Sz22+Sz12+Sx22, Sz12@Sz22+Sx22]
eyeH = [(1/(mps.L-1))*eye(4) for _ in range(5)]
fullH = Sz1@Sz2+Sz2@Sz3+Sz3@Sz4+Sz4@Sz5+Sz5@Sz6+Sx1+Sx2+Sx3+Sx4+Sx5+Sx6
for i, j in product(range(mps.L), range(mps.L)):
## F2 = <d_id_j ψ|H|ψ>
# zero for H = I
self.assertTrue(allclose(mps.F2(i, j, eyeH, testing=True), 0))
# Test gauge projectors are in the right place
mps.right_canonicalise()
l, r = mps.get_envs()
z1 = ncon([mps.F2(i, j, listH, testing=True), l(i-1)@c(mps[i])], [[1, 2, 3, -1, -2, -3], [1, 2, 3]])
z2 = ncon([mps.F2(i, j, listH, testing=True), l(j-1)@c(mps[j])], [[-1, -2, -3, 1, 2, 3], [1, 2, 3]])
self.assertTrue(allclose(z1, 0))
self.assertTrue(allclose(z2, 0))
mps.left_canonicalise()
l, r = mps.get_envs()
z1 = ncon([mps.F2(i, j, listH, testing=True), l(i-1)@c(mps[i])], [[1, 2, 3, -1, -2, -3], [1, 2, 3]])
z2 = ncon([mps.F2(i, j, listH, testing=True), l(j-1)@c(mps[j])], [[-1, -2, -3, 1, 2, 3], [1, 2, 3]])
self.assertTrue(allclose(z1, 0))
self.assertTrue(allclose(z2, 0))
## F1 = <d_iψ|H|d_jψ>
# For H = I: should be equal to δ_{ij} pr(i)
if i!=j:
self.assertTrue(allclose(mps.F1(i, j, eyeH, testing=True), 0))
if i==j:
b = mps.F1(i, j, eyeH, testing=True)
a = ncon([mps.left_null_projector(i), inv(r(i))], [[-1, -2, -4, -5], [-3, -6]])
self.assertTrue(allclose(a, b))
# Test gauge projectors are in the right place
mps.left_canonicalise()
l, r = mps.get_envs()
z1 = td(mps.F1(i, j, listH, testing=True), l(i-1)@c(mps[i]), [[0, 1, 2], [0, 1, 2]])
z1 = td(mps.F1(i, j, listH, testing=True), l(j-1)@mps[j], [[3, 4, 5], [0, 1, 2]])
self.assertTrue(allclose(z1, 0))
self.assertTrue(allclose(z2, 0))
mps.right_canonicalise()
l, r = mps.get_envs()
z1 = td(mps.F1(i, j, listH, testing=True), l(i-1)@c(mps[i]), [[0, 1, 2], [0, 1, 2]])
z1 = td(mps.F1(i, j, listH, testing=True), l(j-1)@mps[j], [[3, 4, 5], [0, 1, 2]])
self.assertTrue(allclose(z1, 0))
self.assertTrue(allclose(z2, 0))
def left_null_projector(self,
n,
l=None,
get_vL=False,
store_envs=False,
vL=None):
"""left_null_projector: |
- inv(sqrt(l)) - vL = vL- inv(sqrt(l))-
|
replaces A(n) in TDVP
:param n: site
"""
if l is None:
l, _ = self.get_envs(store_envs)
if vL is None:
L_ = sw(cT(self[n]) @ ch(l(n - 1)), 0, 1)
L = L_.reshape(-1, self.d * L_.shape[-1])
vL = null(L).reshape((self.d, L.shape[1] // self.d, -1))
pr = ncon([inv(ch(l(n - 1))) @ vL,
inv(ch(l(n - 1))) @ c(vL)], [[-1, -2, 1], [-3, -4, 1]])
if get_vL:
return pr, vL
return pr