def expect_3s(self, op, n):
"""Computes the expectation value of a nearest-neighbour three-site operator.
The operator should be a q[n] x q[n + 1] x q[n + 2] x q[n] x
q[n + 1] x q[n + 2] array such that op[s, t, u, v, w, x] =
<stu|op|vwx> or a function of the form op(s, t, u, v, w, x) =
<stu|op|vwx>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator array or function.
n : int
The leftmost site number (operator acts on n, n + 1, n + 2).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
A = self.A[n]
Ap1 = self.A[n + 1]
Ap2 = self.A[n + 2]
AAA = tm.calc_AAA(A, Ap1, Ap2)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], Ap2.shape[0],
A.shape[0], Ap1.shape[0], Ap2.shape[0]))
C = tm.calc_C_3s_mat_op_AAA(op, AAA)
res = tm.eps_r_op_3s_C123_AAA456(self.r[n + 2], C, AAA)
return m.adot(self.l[n - 1], res)
def expect_3s(self, op, n):
"""Computes the expectation value of a nearest-neighbour three-site operator.
The operator should be a q[n] x q[n + 1] x q[n + 2] x q[n] x
q[n + 1] x q[n + 2] array such that op[s, t, u, v, w, x] =
<stu|op|vwx> or a function of the form op(s, t, u, v, w, x) =
<stu|op|vwx>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator array or function.
n : int
The leftmost site number (operator acts on n, n + 1, n + 2).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
A = self.A[n]
Ap1 = self.A[n + 1]
Ap2 = self.A[n + 2]
AAA = tm.calc_AAA(A, Ap1, Ap2)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], Ap2.shape[0],
A.shape[0], Ap1.shape[0], Ap2.shape[0]))
C = tm.calc_C_3s_mat_op_AAA(op, AAA)
res = tm.eps_r_op_3s_C123_AAA456(self.r[n + 2], C, AAA)
return m.adot(self.l[n - 1], res)
def calc_C(self, n_low=-1, n_high=-1):
"""Generates the C tensors used to calculate the K's and ultimately the B's.
This is called automatically by self.update().
C[n] contains a contraction of the Hamiltonian self.ham with the parameter
tensors over the local basis indices.
This is prerequisite for calculating the tangent vector parameters B,
which optimally approximate the exact time evolution.
These are to be used on one side of the super-operator when applying the
nearest-neighbour Hamiltonian, similarly to C in eqn. (44) of
arXiv:1103.0936v2 [cond-mat.str-el], for the non-norm-preserving case.
Makes use only of the nearest-neighbour Hamiltonian, and of the A's.
C[n] depends on A[n] through A[n + self.ham_sites - 1].
"""
if self.ham is None:
return 0
if n_low < 1:
n_low = 1
if n_high < 1:
n_high = self.N - self.ham_sites + 1
for n in xrange(1, self.N):
self.AA[n] = tm.calc_AA(self.A[n], self.A[n + 1])
if self.ham_sites == 3:
for n in xrange(1, self.N - 1):
self.AAA[n] = tm.calc_AAA_AA(self.AA[n], self.A[n + 2])
else:
self.AAA.fill(None)
for n in xrange(n_low, n_high + 1):
if callable(self.ham):
ham_n = lambda *args: self.ham(n, *args)
ham_n = sp.vectorize(ham_n, otypes=[sp.complex128])
ham_n = sp.fromfunction(ham_n, tuple(self.C[n].shape[:-2] * 2))
else:
ham_n = self.ham[n]
if self.ham_sites == 2:
self.C[n] = tm.calc_C_mat_op_AA(ham_n, self.AA[n])
else:
self.C[n] = tm.calc_C_3s_mat_op_AAA(ham_n, self.AAA[n])
def calc_C(self, n_low=-1, n_high=-1):
"""Generates the C tensors used to calculate the K's and ultimately the B's.
This is called automatically by self.update().
C[n] contains a contraction of the Hamiltonian self.ham with the parameter
tensors over the local basis indices.
This is prerequisite for calculating the tangent vector parameters B,
which optimally approximate the exact time evolution.
These are to be used on one side of the super-operator when applying the
nearest-neighbour Hamiltonian, similarly to C in eqn. (44) of
arXiv:1103.0936v2 [cond-mat.str-el], for the non-norm-preserving case.
Makes use only of the nearest-neighbour Hamiltonian, and of the A's.
C[n] depends on A[n] through A[n + self.ham_sites - 1].
"""
if self.ham is None:
return 0
if n_low < 1:
n_low = 1
if n_high < 1:
n_high = self.N - self.ham_sites + 1
for n in xrange(n_low, n_high + 1):
if callable(self.ham):
ham_n = lambda *args: self.ham(n, *args)
ham_n = sp.vectorize(ham_n, otypes=[sp.complex128])
ham_n = sp.fromfunction(ham_n, tuple(self.C[n].shape[:-2] * 2))
else:
ham_n = self.ham[n]
if self.ham_sites == 2:
AA = tm.calc_AA(self.A[n], self.A[n + 1])
self.C[n] = tm.calc_C_mat_op_AA(ham_n, AA)
else:
AAA = tm.calc_AAA(self.A[n], self.A[n + 1], self.A[n + 2])
self.C[n] = tm.calc_C_3s_mat_op_AAA(ham_n, AAA)
