def calc_K(self):
"""Generates the right K matrices used to calculate the B's
K[n] contains 'column-vectors' such that <l[n]|K[n]> = trace(l[n].dot(K[n])).
K_l[n] contains 'bra-vectors' such that <K_l[n]|r[n]> = trace(K_l[n].dot(r[n])).
"""
self.h_expect = sp.zeros((self.N + 1), dtype=self.typ)
self.uni_r.calc_AA()
self.uni_r.calc_C()
self.uni_r.calc_K()
self.K[self.N + 1][:] = self.uni_r.K[0]
self.uni_l.calc_AA()
self.uni_l.calc_C()
K_left, h_left_uni = self.uni_l.calc_K_l()
self.K_l[0][:] = K_left[-1]
for n in xrange(self.N, self.N_centre - 1, -1):
self.K[n], he = tm.calc_K(self.K[n + 1], self.C[n], self.get_l(n - 1),
self.r[n + 1], self.A[n], self.get_AA(n))
self.h_expect[n] = he
for n in xrange(1, self.N_centre + 1):
self.K_l[n], he = tm.calc_K_l(self.K_l[n - 1], self.C[n - 1], self.get_l(n - 2),
self.r[n], self.A[n], self.get_AA(n - 1))
self.h_expect[n - 1] = he
self.dH_expect = (mm.adot_noconj(self.K_l[self.N_centre], self.r[self.N_centre])
+ mm.adot(self.l[self.N_centre - 1], self.K[self.N_centre])
- (self.N + 1) * self.uni_r.h_expect)
def calc_K(self):
"""Generates the right K matrices used to calculate the B's
K[n] contains 'column-vectors' such that <l[n]|K[n]> = trace(l[n].dot(K[n])).
K_l[n] contains 'bra-vectors' such that <K_l[n]|r[n]> = trace(K_l[n].dot(r[n])).
"""
self.h_expect = sp.zeros((self.N + 1), dtype=self.typ)
self.uni_r.calc_AA()
self.uni_r.calc_C()
self.uni_r.calc_K()
self.K[self.N + 1][:] = self.uni_r.K
self.uni_l.calc_AA()
self.uni_l.calc_C()
K_left, h_left_uni = self.uni_l.calc_K_l()
self.K_l[0][:] = K_left
for n in xrange(self.N, self.N_centre - 1, -1):
self.K[n], he = tm.calc_K(self.K[n + 1],
self.C[n],
self.get_l(n - 1),
self.r[n + 1],
self.A[n],
self.A[n + 1],
sanity_checks=self.sanity_checks)
self.h_expect[n] = he
for n in xrange(1, self.N_centre + 1):
self.K_l[n], he = tm.calc_K_l(self.K_l[n - 1],
self.C[n - 1],
self.get_l(n - 2),
self.r[n],
self.A[n],
self.A[n - 1],
sanity_checks=self.sanity_checks)
self.h_expect[n - 1] = he
self.dH_expect = (
mm.adot_noconj(self.K_l[self.N_centre], self.r[self.N_centre]) +
mm.adot(self.l[self.N_centre - 1], self.K[self.N_centre]) -
(self.N + 1) * self.uni_r.h_expect)
def calc_K(self, n_low=-1, n_high=-1):
"""Generates the K matrices used to calculate the B's.
This is called automatically by self.update().
K[n] is contains the action of the Hamiltonian on sites n to N.
K[n] is recursively defined. It depends on C[m] and A[m] for all m >= n.
It directly depends on A[n], A[n + 1], r[n], r[n + 1], C[n] and K[n + 1].
This is equivalent to K on p. 14 of arXiv:1103.0936v2 [cond-mat.str-el], except
that it is for the non-norm-preserving case.
K[1] is, assuming a normalized state, the expectation value H of Ĥ.
"""
if n_low < 1:
n_low = 1
if n_high < 1:
n_high = self.N
for n in reversed(xrange(n_low, n_high + 1)):
if n <= self.N - self.ham_sites + 1:
if self.ham_sites == 2:
self.K[n], ex = tm.calc_K(self.K[n + 1], self.C[n], self.l[n - 1],
self.r[n + 1], self.A[n], self.A[n + 1],
sanity_checks=self.sanity_checks)
else:
self.K[n], ex = tm.calc_K_3s(self.K[n + 1], self.C[n], self.l[n - 1],
self.r[n + 2], self.A[n], self.A[n + 1],
self.A[n + 2],
sanity_checks=self.sanity_checks)
self.h_expect[n] = ex
else:
self.K[n].fill(0)
if n_low == 1:
self.H_expect = sp.asscalar(self.K[1])
