def restore_CF_dbg(self):
for n in xrange(self.N + 2):
print (n, self.l[n].trace().real, self.r[n].trace().real,
mm.adot(self.l[n], self.r[n]).real)
norm_r = mm.adot(self.uni_r.l[-1], self.r[self.N])
norm_l = mm.adot(self.l[0], self.uni_l.r[-1])
print "norm of uni_r: ", norm_r
print "norm of uni_l: ", norm_l
#r_m1 = self.eps_r(0, self.r[0])
#print mm.adot(self.l[0], r_m1).real
norm = mm.adot(self.l[0], self.r[0]).real
try:
h = sp.empty((self.N + 1), dtype=self.typ)
for n in xrange(self.N + 1):
h[n] = self.expect_2s(self.h_nn[n], n)
h *= 1/norm
#self.uni_l.A = self.A[0] #FIXME: Not sure how to handle this yet...
self.uni_l.l[-1] = self.l[0]
self.uni_l.calc_AA()
h_left = self.uni_l.expect_2s(self.uni_l.ham.copy()) / norm_l
#self.uni_r.A = self.A[self.N + 1]
self.uni_r.r[-1] = self.r[self.N]
self.uni_r.calc_AA()
h_right = self.uni_r.expect_2s(self.uni_r.ham.copy()) / norm_r
return h, h_left, h_right
except AttributeError:
return sp.array([0]), 0, 0
def restore_CF_dbg(self):
for n in xrange(self.N + 2):
print (n, self.l[n].trace().real, self.r[n].trace().real,
mm.adot(self.l[n], self.r[n]).real)
norm_r = mm.adot(self.uni_r.l, self.r[self.N])
norm_l = mm.adot(self.l[0], self.uni_l.r)
print "norm of uni_r: ", norm_r
print "norm of uni_l: ", norm_l
#r_m1 = self.eps_r(0, self.r[0])
#print mm.adot(self.l[0], r_m1).real
norm = mm.adot(self.l[0], self.r[0]).real
h = sp.empty((self.N + 1), dtype=self.typ)
for n in xrange(self.N + 1):
h[n] = self.expect_2s(self.h_nn[n], n)
h *= 1/norm
self.uni_l.A = self.A[0]
self.uni_l.l = self.l[0]
self.uni_l.calc_AA()
h_left = self.uni_l.expect_2s(self.uni_l.ham.copy()) / norm_l
self.uni_r.A = self.A[self.N + 1]
self.uni_r.r = self.r[self.N]
self.uni_r.calc_AA()
h_right = self.uni_l.expect_2s(self.uni_r.ham.copy()) / norm_r
return h, h_left, h_right
def restore_CF_dbg(self):
for n in xrange(self.N + 2):
print(n, self.l[n].trace().real, self.r[n].trace().real,
mm.adot(self.l[n], self.r[n]).real)
norm_r = mm.adot(self.uni_r.l[-1], self.r[self.N])
norm_l = mm.adot(self.l[0], self.uni_l.r[-1])
print "norm of uni_r: ", norm_r
print "norm of uni_l: ", norm_l
#r_m1 = self.eps_r(0, self.r[0])
#print mm.adot(self.l[0], r_m1).real
norm = mm.adot(self.l[0], self.r[0]).real
try:
h = sp.empty((self.N + 1), dtype=self.typ)
for n in xrange(self.N + 1):
h[n] = self.expect_2s(self.h_nn[n], n)
h *= 1 / norm
#self.uni_l.A = self.A[0] #FIXME: Not sure how to handle this yet...
self.uni_l.l[-1] = self.l[0]
self.uni_l.calc_AA()
h_left = self.uni_l.expect_2s(self.uni_l.ham.copy()) / norm_l
#self.uni_r.A = self.A[self.N + 1]
self.uni_r.r[-1] = self.r[self.N]
self.uni_r.calc_AA()
h_right = self.uni_r.expect_2s(self.uni_r.ham.copy()) / norm_r
return h, h_left, h_right
except AttributeError:
return sp.array([0]), 0, 0
def calc_B1(self):
"""Calculate the optimal B1 given right gauge-fixing on B2..N and
no gauge-fixing on B1.
We use the non-norm-preserving K's, since the norm-preservation
is not needed elsewhere. It is cleaner to subtract the relevant
norm-changing terms from the K's here than to generate all K's
with norm-preservation.
"""
B1 = sp.empty_like(self.A[1])
try:
r1_i = self.r[1].inv()
except AttributeError:
r1_i = mm.invmh(self.r[1])
try:
l0_i = self.l[0].inv()
except AttributeError:
l0_i = mm.invmh(self.l[0])
A0 = self.A[0]
A1 = self.A[1]
A2 = self.A[2]
r1 = self.r[1]
r2 = self.r[2]
l0 = self.l[0]
KLh = mm.H(self.u_gnd_l.K_left - l0 * mm.adot(self.u_gnd_l.K_left, self.r[0]))
K2 = self.K[2] - r1 * mm.adot(self.l[1], self.K[2])
C1 = self.C[1] - self.h_expect[1] * self.AA1
C0 = self.C[0] - self.h_expect[0] * self.AA0
for s in xrange(self.q[1]):
try:
B1[s] = A1[s].dot(r1_i.dot_left(K2))
except AttributeError:
B1[s] = A1[s].dot(K2.dot(r1_i))
for t in xrange(self.q[2]):
try:
B1[s] += C1[s, t].dot(r2.dot(r1_i.dot_left(mm.H(A2[t]))))
except AttributeError:
B1[s] += C1[s, t].dot(r2.dot(mm.H(A2[t]).dot(r1_i)))
B1sbit = KLh.dot(A1[s])
for t in xrange(self.q[0]):
B1sbit += mm.H(A0[t]).dot(l0.dot(C0[t,s]))
B1[s] += l0_i.dot(B1sbit)
rb = sp.zeros_like(self.r[0])
for s in xrange(self.q[1]):
rb += B1[s].dot(r1.dot(mm.H(B1[s])))
eta = sp.sqrt(mm.adot(l0, rb))
return B1, eta
def calc_K(self):
"""Generates the right K matrices used to calculate the B's
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.
Return the excess energy.
"""
n_low = 0
n_high = self.N + 1
H = mm.H
self.h_expect = sp.zeros((self.N + 1), dtype=self.typ)
self.u_gnd_r.calc_AA()
self.u_gnd_r.calc_C()
self.u_gnd_r.calc_K()
self.K[self.N + 1][:] = self.u_gnd_r.K
for n in reversed(xrange(n_low, n_high)):
self.K[n].fill(0)
K = self.K[n]
Kp1 = self.K[n + 1]
C = self.C[n]
rp1 = self.r[n + 1]
A = self.A[n]
Ap1 = self.A[n + 1]
Hr = sp.zeros_like(K)
for s in xrange(self.q[n]):
Ash = H(A[s])
for t in xrange(self.q[n+1]):
Hr += C[s, t].dot(rp1.dot(H(Ap1[t]).dot(Ash)))
K += A[s].dot(Kp1.dot(Ash))
self.h_expect[n] = mm.adot(self.get_l(n), Hr)
K += Hr
self.u_gnd_l.calc_AA()
self.u_gnd_l.calc_C()
K_left, h_left_uni = self.u_gnd_l.calc_K_l()
h = (mm.adot(K_left, self.r[0]) + mm.adot(self.l[0], self.K[0])
- (self.N + 1) * self.u_gnd_r.h)
return h
def density_2s(self, d):
"""Returns a reduced density matrix for a pair of (seperated) sites.
The site number basis is used: rho[s * q + u, t * q + v]
with 0 <= s, t < q and 0 <= u, v < q.
The state must be up-to-date -- see self.update()!
Parameters
----------
d : int
The distance between the first and the second sites considered (d = n2 - n1).
Returns
-------
rho : ndarray
Reduced density matrix in the number basis.
"""
rho = sp.empty((self.q * self.q, self.q * self.q), dtype=sp.complex128)
for s2 in xrange(self.q):
for t2 in xrange(self.q):
r_n2 = m.mmul(self.A[t2], self.r, m.H(self.A[s2]))
r_n = r_n2
for n in xrange(d - 1):
r_n = tm.eps_r_noop(r_n, self.A, self.A)
for s1 in xrange(self.q):
for t1 in xrange(self.q):
r_n1 = m.mmul(self.A[t1], r_n, m.H(self.A[s1]))
tmp = m.adot(self.l, r_n1)
rho[s1 * self.q + s2, t1 * self.q + t2] = tmp
return rho
def expect_2s(self, op):
"""Computes the expectation value of a nearest-neighbour two-site operator.
The operator should be a q x q x q x q array
such that op[s, t, u, v] = <st|op|uv> or a function of the form
op(s, t, u, v) = <st|op|uv>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator array or function.
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
if callable(op):
op = np.vectorize(op, otypes=[np.complex128])
op = np.fromfunction(op, (self.q, self.q, self.q, self.q))
C = tm.calc_C_mat_op_AA(op, self.AA)
res = tm.eps_r_op_2s_C12_AA34(self.r, C, self.AA)
return m.adot(self.l, res)
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 expect_2s(self, op, n):
"""Computes the expectation value of a nearest-neighbour two-site operator.
The operator should be a q[n] x q[n + 1] x q[n] x q[n + 1] array
such that op[s, t, u, v] = <st|op|uv> or a function of the form
op(s, t, u, v) = <st|op|uv>.
Parameters
----------
o : ndarray or callable
The operator array or function.
n : int
The leftmost site number (operator acts on n, n + 1).
"""
A = self.get_A(n)
Ap1 = self.get_A(n + 1)
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.get_r(n + 1), C, AA)
return mm.adot(self.get_l(n - 1), res)
def expect_2s(self, op, n, AA=None):
"""Computes the expectation value of a nearest-neighbour two-site operator.
The operator should be a q[n] x q[n + 1] x q[n] x q[n + 1] array
such that op[s, t, u, v] = <st|op|uv> or a function of the form
op(s, t, u, v) = <st|op|uv>.
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).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
A = self.A[n]
Ap1 = self.A[n + 1]
if AA is None:
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.r[n + 1], C, AA)
return m.adot(self.l[n - 1], res)
def _excite_expect_2s_tp_sep(AL, AR, B, lL, rR, op, d, n1, n2):
ls = [None] * (d + 1)
ls[0] = lL
rs = [None] * (d + 1)
rs[-1] = rR
As1 = [None] + [AL] * (n1 - 1) + [B] + [AR] * (d - n1 + 1)
As2 = [None] + [AL] * (n2 - 1) + [B] + [AR] * (d - n2 + 1)
for n in xrange(1, d):
ls[n] = tm.eps_l_noop(ls[n - 1], As1[n], As2[n])
for n in xrange(d, 0, -1):
rs[n - 1] = tm.eps_r_noop(rs[n], As1[n], As2[n])
Cs1 = [None] * (d + 1)
for n in xrange(1, d):
Cs1[n] = tm.calc_C_tp(op, As1[n], As1[n + 1])
res = [
m.adot(ls[n - 1],
tm.eps_r_op_2s_C12_tp(rs[n + 1], Cs1[n], As2[n], As2[n + 1]))
for n in xrange(1, d)
]
return sp.array(res)
def expect_1s(self, op):
"""Computes the expectation value of a single-site operator.
The operator should be a self.q x self.q matrix or generating function
such that op[s, t] or op(s, t) equals <s|op|t>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator.
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
if callable(op):
op = np.vectorize(op, otypes=[np.complex128])
op = np.fromfunction(op, (self.q, self.q))
Or = tm.eps_r_op_1s(self.r, self.A, self.A, op)
return m.adot(self.l, Or)
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_BB_Y_2s_ham_3s(A_m1, A_p2, C, C_m1, Vlh, Vrh_p1, l_m2, r_p2, l_s_m1,
l_si_m1, r_s_p1, r_si_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Vrri_p1 = sp.zeros_like(Vr_p1)
try:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = r_si_p1.dot_left(Vr_p1[s])
except AttributeError:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = Vr_p1[s].dot(r_si_p1)
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj()
liVl = sp.zeros_like(Vl)
for s in xrange(liVl.shape[0]):
liVl[s] = l_si_m1.dot(Vl[s])
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=Vrh_p1.dtype)
if not A_p2 is None:
for s in xrange(C.shape[0]):
Y += Vlh[s].dot(
l_s_m1.dot(eps_r_op_2s_C12(r_p2, C[s], Vrri_p1, A_p2)))
if not A_m1 is None:
for u in xrange(C_m1.shape[2]):
Y += eps_l_op_2s_A1_A2_C34(l_m2, A_m1, liVl,
C_m1[:, :,
u]).dot(r_s_p1.dot(Vrh_p1[u]))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def density_2s(self, n1, n2):
"""Returns a reduced density matrix for a pair of sites.
Currently only supports sites in the nonuniform window.
Parameters
----------
n1 : int
The site number of the first site.
n2 : int
The site number of the second site (must be > n1).
"""
rho = sp.empty((self.q[n1] * self.q[n2], self.q[n1] * self.q[n2]),
dtype=sp.complex128)
r_n2 = sp.empty_like(self.r[n2 - 1])
r_n1 = sp.empty_like(self.r[n1 - 1])
ln1m1 = self.get_l(n1 - 1)
for s2 in xrange(self.q[n2]):
for t2 in xrange(self.q[n2]):
r_n2 = mm.mmul(self.A[n2][t2], self.r[n2],
mm.H(self.A[n2][s2]))
r_n = r_n2
for n in reversed(xrange(n1 + 1, n2)):
r_n = tm.eps_r_noop(r_n, self.A[n], self.A[n])
for s1 in xrange(self.q[n1]):
for t1 in xrange(self.q[n1]):
r_n1 = mm.mmul(self.A[n1][t1], r_n,
mm.H(self.A[n1][s1]))
tmp = mm.adot(ln1m1, r_n1)
rho[s1 * self.q[n1] + s2, t1 * self.q[n1] + t2] = tmp
return rho
def expect_2s(self, op, n, AA=None):
"""Computes the expectation value of a nearest-neighbour two-site operator.
The operator should be a q[n] x q[n + 1] x q[n] x q[n + 1] array
such that op[s, t, u, v] = <st|op|uv> or a function of the form
op(s, t, u, v) = <st|op|uv>.
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).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
A = self.A[n]
Ap1 = self.A[n + 1]
if AA is None:
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.r[n + 1], C, AA)
return m.adot(self.l[n - 1], res)
def calc_BB_Y_2s_ham_3s(A_m1, A_p2, C, C_m1, Vlh, Vrh_p1, l_m2, r_p2, l_s_m1, l_si_m1, r_s_p1, r_si_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Vrri_p1 = sp.zeros_like(Vr_p1)
try:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = r_si_p1.dot_left(Vr_p1[s])
except AttributeError:
for s in xrange(Vrri_p1.shape[0]):
Vrri_p1[s] = Vr_p1[s].dot(r_si_p1)
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj()
liVl = sp.zeros_like(Vl)
for s in xrange(liVl.shape[0]):
liVl[s] = l_si_m1.dot(Vl[s])
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=Vrh_p1.dtype)
if not A_p2 is None:
for s in xrange(C.shape[0]):
Y += Vlh[s].dot(l_s_m1.dot(eps_r_op_2s_C12(r_p2, C[s], Vrri_p1, A_p2)))
if not A_m1 is None:
for u in xrange(C_m1.shape[2]):
Y += eps_l_op_2s_A1_A2_C34(l_m2, A_m1, liVl, C_m1[:, :, u]).dot(r_s_p1.dot(Vrh_p1[u]))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
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 density_1s(self, n):
"""Returns a reduced density matrix for a single site.
The site number basis is used: rho[s, t]
with 0 <= s, t < q[n].
The state must be up-to-date -- see self.update()!
Parameters
----------
n1 : int
The site number.
Returns
-------
rho : ndarray
Reduced density matrix in the number basis.
"""
rho = sp.empty((self.q[n], self.q[n]), dtype=sp.complex128)
r_n = self.r[n]
r_nm1 = sp.empty_like(self.r[n - 1])
for s in xrange(self.q[n]):
for t in xrange(self.q[n]):
r_nm1 = m.mmul(self.A[n][t], r_n, m.H(self.A[n][s]))
rho[s, t] = m.adot(self.l[n - 1], r_nm1)
return rho
def expect_2s(self, op, n):
"""Computes the expectation value of a nearest-neighbour two-site operator.
The operator should be a q[n] x q[n + 1] x q[n] x q[n + 1] array
such that op[s, t, u, v] = <st|op|uv> or a function of the form
op(s, t, u, v) = <st|op|uv>.
Parameters
----------
o : ndarray or callable
The operator array or function.
n : int
The leftmost site number (operator acts on n, n + 1).
"""
A = self.get_A(n)
Ap1 = self.get_A(n + 1)
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(
op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.get_r(n + 1), C, AA)
return mm.adot(self.get_l(n - 1), res)
def expect_1s(self, op, n):
"""Computes the expectation value of a single-site operator.
The operator should be a q[n] x q[n] matrix or generating function
such that op[s, t] or op(s, t) equals <s|op|t>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator.
n : int
The site number (1 <= n <= N).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q[n], self.q[n]))
res = tm.eps_r_op_1s(self.r[n], self.A[n], self.A[n], op)
return m.adot(self.l[n - 1], res)
def density_1s(self, n):
"""Returns a reduced density matrix for a single site.
The site number basis is used: rho[s, t]
with 0 <= s, t < q[n].
The state must be up-to-date -- see self.update()!
Parameters
----------
n1 : int
The site number.
Returns
-------
rho : ndarray
Reduced density matrix in the number basis.
"""
rho = sp.empty((self.q[n], self.q[n]), dtype=sp.complex128)
r_n = self.r[n]
r_nm1 = sp.empty_like(self.r[n - 1])
for s in xrange(self.q[n]):
for t in xrange(self.q[n]):
r_nm1 = m.mmul(self.A[n][t], r_n, m.H(self.A[n][s]))
rho[s, t] = m.adot(self.l[n - 1], r_nm1)
return rho
def calc_B_1s_diss(self, op, n):
"""Applies a single-site operator to a single site and returns
the parameter tensor for that site after the change with the
change in the norm of the state projected out.
Parameters
----------
op : ndarray or callable
The single-site operator. See self.expect_1s().
n: int
The site to apply the operator to.
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q[n], self.q[n]))
newAn = sp.zeros_like(self.A[n])
for s in xrange(self.q[n]):
for t in xrange(self.q[n]):
newAn[s] += self.A[n][t] * op[s, t]
r_nm1 = TDVP.tm.eps_r_noop(self.r[n], newAn, newAn)
ev = mm.adot(self.l[n - 1], r_nm1)
newAn -= ev * self.A[n] #norm-fixing
return newAn
def expect_3s(self, op, n, AAA=None):
"""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)
"""
if AAA is None:
if not self.AAA[n] is None:
AAA = self.AAA[n]
else:
AAA = tm.calc_AAA_AA(self.AA[n], self.A[n + 2])
if op is self.ham[n] and self.ham_sites == 3:
res = tm.eps_r_op_3s_C123_AAA456(self.r[n + 2], self.C[n], AAA)
return m.adot(self.l[n - 1], res)
else:
return super(EvoMPS_MPS_Generic).expect_3s(op, n, AAA=AAA)
def expect_1s(self, op, n):
"""Computes the expectation value of a single-site operator.
The operator should be a q[n] x q[n] matrix or generating function
such that op[s, t] or op(s, t) equals <s|op|t>.
The state must be up-to-date -- see self.update()!
Parameters
----------
op : ndarray or callable
The operator.
n : int
The site number (1 <= n <= N).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q[n], self.q[n]))
res = tm.eps_r_op_1s(self.r[n], self.A[n], self.A[n], op)
return m.adot(self.l[n - 1], res)
def density_2s(self, n1, n2):
"""Returns a reduced density matrix for a pair of sites.
Currently only supports sites in the nonuniform window.
Parameters
----------
n1 : int
The site number of the first site.
n2 : int
The site number of the second site (must be > n1).
"""
rho = sp.empty((self.q[n1] * self.q[n2], self.q[n1] * self.q[n2]), dtype=sp.complex128)
r_n2 = sp.empty_like(self.r[n2 - 1])
r_n1 = sp.empty_like(self.r[n1 - 1])
ln1m1 = self.get_l(n1 - 1)
for s2 in xrange(self.q[n2]):
for t2 in xrange(self.q[n2]):
r_n2 = mm.mmul(self.A[n2][t2], self.r[n2], mm.H(self.A[n2][s2]))
r_n = r_n2
for n in reversed(xrange(n1 + 1, n2)):
r_n = tm.eps_r_noop(r_n, self.A[n], self.A[n])
for s1 in xrange(self.q[n1]):
for t1 in xrange(self.q[n1]):
r_n1 = mm.mmul(self.A[n1][t1], r_n, mm.H(self.A[n1][s1]))
tmp = mm.adot(ln1m1, r_n1)
rho[s1 * self.q[n1] + s2, t1 * self.q[n1] + t2] = tmp
return rho
def expect_1s_1s(self, op1, op2, n1, n2, return_intermediates=False):
"""Computes the expectation value of two single site operators acting
on two different sites.
The result is < op1 op2 >.
See expect_1s().
Requires n1 < n2.
The state must be up-to-date -- see self.update()!
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
n1 : int
The site number of the first site.
n2 : int
The site number of the second site (must be > n1).
return_intermediates : bool
Whether to return results for intermediate sites.
Returns
-------
expval : complex128 or sequence of complex128
The expectation value (data type may be complex), or values if
return_intermediates == True.
"""
if callable(op1):
op1 = sp.vectorize(op1, otypes=[sp.complex128])
op1 = sp.fromfunction(op1, (self.q[n1], self.q[n1]))
if callable(op2):
op2 = sp.vectorize(op2, otypes=[sp.complex128])
op2 = sp.fromfunction(op2, (self.q[n2], self.q[n2]))
d = n2 - n1
res = sp.zeros((d + 1), dtype=sp.complex128)
lj = tm.eps_l_op_1s(self.l[n1 - 1], self.A[n1], self.A[n1], op1)
if return_intermediates:
res[0] = self.expect_1s(op1.dot(op1), n1)
for j in xrange(1, d + 1):
if return_intermediates or j == d:
lj_op = tm.eps_l_op_1s(lj, self.A[n1 + j], self.A[n1 + j], op2)
res[j] = m.adot(lj_op, self.r[n1 + j])
if j < d:
lj = tm.eps_l_noop(lj, self.A[n1 + j], self.A[n1 + j])
if return_intermediates:
return res
else:
return res[-1]
def expect_1s_1s(self, op1, op2, n1, n2, return_intermediates=False):
"""Computes the expectation value of two single site operators acting
on two different sites.
The result is < op1 op2 >.
See expect_1s().
Requires n1 < n2.
The state must be up-to-date -- see self.update()!
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
n1 : int
The site number of the first site.
n2 : int
The site number of the second site (must be > n1).
return_intermediates : bool
Whether to return results for intermediate sites.
Returns
-------
expval : complex128 or sequence of complex128
The expectation value (data type may be complex), or values if
return_intermediates == True.
"""
if callable(op1):
op1 = sp.vectorize(op1, otypes=[sp.complex128])
op1 = sp.fromfunction(op1, (self.q[n1], self.q[n1]))
if callable(op2):
op2 = sp.vectorize(op2, otypes=[sp.complex128])
op2 = sp.fromfunction(op2, (self.q[n2], self.q[n2]))
d = n2 - n1
res = sp.zeros((d + 1), dtype=sp.complex128)
lj = tm.eps_l_op_1s(self.l[n1 - 1], self.A[n1], self.A[n1], op1)
if return_intermediates:
res[0] = self.expect_1s(op1.dot(op1), n1)
for j in xrange(1, d + 1):
if return_intermediates or j == d:
lj_op = tm.eps_l_op_1s(lj, self.A[n1 + j], self.A[n1 + j], op2)
res[j] = m.adot(lj_op, self.r[n1 + j])
if j < d:
lj = tm.eps_l_noop(lj, self.A[n1 + j], self.A[n1 + j])
if return_intermediates:
return res
else:
return res[-1]
def matvec(self, v):
x = v.reshape((self.D, self.D))
if self.left:
xE = self.tdvp._eps_l_noop_dense_A(x, self.out)
QEQ = xE - m.H(self.l) * m.adot(self.r, x)
else:
Ex = self.tdvp._eps_r_noop_dense_A(x, self.out)
QEQ = Ex - self.r * m.adot(self.l, x)
if not self.p == 0:
QEQ *= np.exp(1.j * self.p)
res = x - QEQ
return res.ravel()
def calc_BB_Y_2s(C, Vlh, Vrh_p1, l_s_m1, r_s_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=C.dtype)
for s in xrange(Vlh.shape[0]):
Y += Vlh[s].dot(l_s_m1.dot(eps_r_noop(r_s_p1, C[s], Vr_p1)))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def calc_K_tp(Kp1, lm1, rp1, A, Ap1, C_tp):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_2s_C12_tp(rp1, C_tp, A, Ap1)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def calc_K_3s(Kp1, C, lm1, rp2, A, AAp1Ap2):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_3s_C123_AAA456(rp2, C, AAp1Ap2)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def matvec(self, v):
x = v.reshape((self.D, self.D))
if self.left: #Multiplying from the left, but x is a col. vector, so use mat_dagger
Ehx = tm.eps_l_noop_inplace(x, self.A1, self.A2, self.out)
if self.pseudo:
QEQhx = Ehx - self.l * m.adot(self.r, x)
res = x - sp.exp(-1.j * self.p) * QEQhx
else:
res = x - sp.exp(-1.j * self.p) * Ehx
else:
Ex = tm.eps_r_noop_inplace(x, self.A1, self.A2, self.out)
if self.pseudo:
QEQx = Ex - self.r * m.adot(self.l, x)
res = x - sp.exp(1.j * self.p) * QEQx
else:
res = x - sp.exp(1.j * self.p) * Ex
return res.ravel()
def calc_K(Kp1, C, lm1, rp1, A, AAp1):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_2s_C12_AA34(rp1, C, AAp1)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def calc_K_tp(Kp1, lm1, rp1, A, Ap1, C_tp):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_2s_C12_tp(rp1, C_tp, A, Ap1)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def matvec(self, v):
x = v.reshape((self.D, self.D))
res = self.tmp
out = self.out
res[:] = x
if self.left: # Multiplying from the left, but x is a col. vector, so use mat_dagger
for k in xrange(len(self.A1)):
out = tm.eps_l_noop_inplace(res, self.A1[k], self.A2[k], out)
tmp = res
res = out
out = tmp
if self.pseudo:
out[:] = self.lL
out *= m.adot(self.rL, x)
res -= out
res *= -sp.exp(-1.0j * self.p)
res += x
else:
res *= -sp.exp(-1.0j * self.p)
res += x
else:
for k in xrange(len(self.A1) - 1, -1, -1):
out = tm.eps_r_noop_inplace(res, self.A1[k], self.A2[k], out)
tmp = res
res = out
out = tmp
if self.pseudo:
out[:] = self.rL
out *= m.adot(self.lL, x)
res -= out
res *= -sp.exp(1.0j * self.p)
res += x
else:
res *= -sp.exp(1.0j * self.p)
res += x
return (
res.copy().ravel()
) # apparently we can't reuse the memory we return (seems to blow up lgmres), so we make a copy
def calc_BB_Y_2s(C, Vlh, Vrh_p1, l_s_m1, r_s_p1):
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj()
Y = sp.zeros((Vlh.shape[1], Vrh_p1.shape[2]), dtype=C.dtype)
for s in xrange(Vlh.shape[0]):
Y += Vlh[s].dot(l_s_m1.dot(eps_r_noop(r_s_p1, C[s], Vr_p1)))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def calc_K(Kp1, C, lm1, rp1, A, AAp1):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_2s_C12_AA34(rp1, C, AAp1)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def calc_K_3s(Kp1, C, lm1, rp2, A, AAp1Ap2):
K = eps_r_noop(Kp1, A, A)
Hr = eps_r_op_3s_C123_AAA456(rp2, C, AAp1Ap2)
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def matvec(self, v):
x = v.reshape((self.D, self.D))
if self.left: #Multiplying from the left, but x is a col. vector, so use mat_dagger
Ehx = tm.eps_l_noop_inplace(x, self.A1, self.A2, self.out)
if self.pseudo:
QEQhx = Ehx - self.l * m.adot(self.r, x)
res = x - sp.exp(-1.j * self.p) * QEQhx
else:
res = x - sp.exp(-1.j * self.p) * Ehx
else:
Ex = tm.eps_r_noop_inplace(x, self.A1, self.A2, self.out)
if self.pseudo:
QEQx = Ex - self.r * m.adot(self.l, x)
res = x - sp.exp(1.j * self.p) * QEQx
else:
res = x - sp.exp(1.j * self.p) * Ex
return res.ravel()
def calc_K(self):
Hr = np.zeros_like(self.A[0])
for s in xrange(self.q):
for t in xrange(self.q):
Hr += m.mmul(self.C[s, t], self.r, m.H(self.AA[s, t]))
self.h = m.adot(self.l, Hr)
QHr = Hr - self.r * self.h
self.calc_PPinv(QHr, out=self.K)
if self.sanity_checks:
Ex = self.eps_r(self.K)
QEQ = Ex - self.r * m.adot(self.l, self.K)
res = self.K - QEQ
if not np.allclose(res, QHr):
print "Sanity check failed: Bad K!"
print "Off by: " + str(la.norm(res - QHr))
def calc_BB_Y_2s_tp(C_tp, Vlh, Vrh_p1, l_s_m1, r_s_p1):
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj().copy()
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj().copy()
Y = 0
for al in xrange(len(C_tp)):
Y += eps_l_noop(l_s_m1, Vl, C_tp[al][0]).dot(eps_r_noop(r_s_p1, C_tp[al][1], Vr_p1))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def matvec(self, v):
x = v.reshape((self.D, self.D))
res = self.tmp
out = self.out
res[:] = x
if self.left: #Multiplying from the left, but x is a col. vector, so use mat_dagger
for k in xrange(len(self.A1)):
out = tm.eps_l_noop_inplace(res, self.A1[k], self.A2[k], out)
tmp = res
res = out
out = tmp
if self.pseudo:
out[:] = self.lL
out *= m.adot(self.rL, x)
res -= out
res *= -sp.exp(-1.j * self.p)
res += x
else:
res *= -sp.exp(-1.j * self.p)
res += x
else:
for k in xrange(len(self.A1) - 1, -1, -1):
out = tm.eps_r_noop_inplace(res, self.A1[k], self.A2[k], out)
tmp = res
res = out
out = tmp
if self.pseudo:
out[:] = self.rL
out *= m.adot(self.lL, x)
res -= out
res *= -sp.exp(1.j * self.p)
res += x
else:
res *= -sp.exp(1.j * self.p)
res += x
return res.copy().ravel() #apparently we can't reuse the memory we return (seems to blow up lgmres), so we make a copy
def simple_renorm(self, update_lr=True):
"""Renormalizes the state in by multiplying one of the parameter
tensors by a factor.
"""
norm = mm.adot(self.l[self.N_centre - 1], self.r[self.N_centre - 1])
if abs(1 - norm) > 1E-15:
self.A[self.N_centre] *= 1 / sp.sqrt(norm)
if update_lr:
self.calc_l(n_low=self.N_centre)
self.calc_r(n_high=self.N_centre)
def simple_renorm(self, update_lr=True):
"""Renormalizes the state in by multiplying one of the parameter
tensors by a factor.
"""
norm = mm.adot(self.l[self.N_centre - 1], self.r[self.N_centre - 1])
if abs(1 - norm) > 1E-15:
self.A[self.N_centre] *= 1 / sp.sqrt(norm)
if update_lr:
self.calc_l(n_low=self.N_centre)
self.calc_r(n_high=self.N_centre)
def calc_BB_Y_2s_tp(C_tp, Vlh, Vrh_p1, l_s_m1, r_s_p1):
Vl = sp.transpose(Vlh, axes=(0, 2, 1)).conj().copy()
Vr_p1 = sp.transpose(Vrh_p1, axes=(0, 2, 1)).conj().copy()
Y = 0
for al in xrange(len(C_tp)):
Y += eps_l_noop(l_s_m1, Vl,
C_tp[al][0]).dot(eps_r_noop(r_s_p1, C_tp[al][1],
Vr_p1))
etaBB_sq = mm.adot(Y, Y)
return Y, etaBB_sq
def calc_K_l(self):
lH = np.zeros_like(self.A[0])
for s in xrange(self.q):
for t in xrange(self.q):
lH += m.mmul(m.H(self.AA[s, t]), self.l, self.C[s, t])
h = m.adot(lH, self.r)
lHQ = lH - self.l * h
self.K_left = self.calc_PPinv(lHQ, left=True, out=self.K_left)
if self.sanity_checks:
xE = self.eps_l(self.K_left)
QEQ = xE - self.l * m.adot(self.K_left, self.r)
res = self.K_left - QEQ
if not np.allclose(res, lHQ):
print "Sanity check failed: Bad K_left!"
print "Off by: " + str(la.norm(res - lHQ))
return self.K_left, h
def matvec(self, v):
x = v.reshape((self.D, self.D))
if self.left: #Multiplying from the left, but x is a col. vector, so use mat_dagger
Ehx = x
for k in xrange(len(self.A1)):
Ehx = tm.eps_l_noop(Ehx, self.A1[k], self.A2[k])
if self.pseudo:
QEQhx = Ehx - self.lL * m.adot(self.rL, x)
res = x - sp.exp(-1.j * self.p) * QEQhx
else:
res = x - sp.exp(-1.j * self.p) * Ehx
else:
Ex = x
for k in xrange(len(self.A1) - 1, -1, -1):
Ex = tm.eps_r_noop(Ex, self.A1[k], self.A2[k])
if self.pseudo:
QEQx = Ex - self.rL * m.adot(self.lL, x)
res = x - sp.exp(1.j * self.p) * QEQx
else:
res = x - sp.exp(1.j * self.p) * Ex
return res.ravel()
def f(tau, *args):
if tau < 0:
if use_tangvec_overlap:
res = tau**2 + self.eta_sq.sum().real
else:
res = tau**2 + h_expect_0.real
log.debug((tau, res, "punishing negative tau!"))
taus.append(tau)
ress.append(res)
hs.append(h_expect_0.real)
return res
try:
i = taus.index(tau)
log.debug((tau, ress[i], "from stored"))
return ress[i]
except ValueError:
for n in xrange(1, self.N + 1):
if not Bs[n] is None:
self.A[n] = As0[n] - tau * Bs[n]
if use_tangvec_overlap:
self.update(restore_CF=False)
Bsg = self.calc_B(set_eta=False)
res = 0
for n in xrange(1, self.N + 1):
if not Bs[n] is None:
res += abs(m.adot(self.l[n - 1], tm.eps_r_noop(self.r[n], Bsg[n], Bs[n])))
h_exp = self.H_expect.real
else:
self.calc_l()
self.calc_r()
self.simple_renorm()
self.calc_C()
h_exp = 0
if self.ham_sites == 2:
for n in xrange(1, self.N):
h_exp += self.expect_2s(self.ham[n], n).real
else:
for n in xrange(1, self.N - 1):
h_exp += self.expect_3s(self.ham[n], n).real
res = h_exp
log.debug((tau, res, h_exp, h_exp - h_expect_0.real))
taus.append(tau)
ress.append(res)
hs.append(h_exp)
return res
def expect_string_1s(self, op, n, d):
"""Calculates the expectation values of finite strings
with lengths 1 to d, starting at position n.
"""
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (self.q, self.q))
res = sp.zeros((d), dtype=self.A[1].dtype)
x = self.l[n - 1]
for j in xrange(n, n + d + 1):
Aop = sp.tensordot(op, self.A[j], axes=([1],[0]))
x = tm.eps_l_noop(x, self.A[j], Aop)
res[j - n - 1] = m.adot(x, self.r[j])
return res
def expect_1s_1s(self, op1, op2, d):
"""Computes the expectation value of two single site operators acting
on two different sites.
The result is < op1_n op2_n+d > with the operators acting on sites
n and n + d.
See expect_1s().
Requires d > 0.
The state must be up-to-date -- see self.update()!
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
d : int
The distance (number of sites) between the two sites acted on non-trivially.
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
assert d > 0, 'd must be greater than 1'
if callable(op1):
op1 = sp.vectorize(op1, otypes=[sp.complex128])
op1 = sp.fromfunction(op1, (self.q, self.q))
if callable(op2):
op2 = sp.vectorize(op2, otypes=[sp.complex128])
op2 = sp.fromfunction(op2, (self.q, self.q))
r_n = tm.eps_r_op_1s(self.r, self.A, self.A, op2)
for n in xrange(d - 1):
r_n = tm.eps_r_noop(r_n, self.A, self.A)
r_n = tm.eps_r_op_1s(r_n, self.A, self.A, op1)
return m.adot(self.l, r_n)
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 density_1s(self):
"""Returns a reduced density matrix for a single site.
The site number basis is used: rho[s, t]
with 0 <= s, t < q.
The state must be up-to-date -- see self.update()!
Returns
-------
rho : ndarray
Reduced density matrix in the number basis.
"""
rho = np.empty((self.q, self.q), dtype=self.typ)
for s in xrange(self.q):
for t in xrange(self.q):
rho[s, t] = m.adot(self.l, m.mmul(self.A[t], self.r, m.H(self.A[s])))
return rho
def expect_1s_1s(self, op1, op2, n1, n2):
"""Computes the expectation value of two single site operators acting
on two different sites.
The result is < op1 op2 >.
See expect_1s().
Requires n1 < n2.
The state must be up-to-date -- see self.update()!
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
n1 : int
The site number of the first site.
n2 : int
The site number of the second site (must be > n1).
Returns
-------
expval : floating point number
The expectation value (data type may be complex)
"""
if callable(op1):
op1 = sp.vectorize(op1, otypes=[sp.complex128])
op1 = sp.fromfunction(op1, (self.q[n1], self.q[n1]))
if callable(op2):
op2 = sp.vectorize(op2, otypes=[sp.complex128])
op2 = sp.fromfunction(op2, (self.q[n2], self.q[n2]))
r_n = tm.eps_r_op_1s(self.r[n2], self.A[n2], self.A[n2], op2)
for n in reversed(xrange(n1 + 1, n2)):
r_n = tm.eps_r_noop(r_n, self.A[n], self.A[n])
r_n = tm.eps_r_op_1s(r_n, self.A[n1], self.A[n1], op1)
return m.adot(self.l[n1 - 1], r_n)
def calc_K_common(self, Kp1, C, lm1, rp1, A, Ap1):
Dm1 = A.shape[1]
q = A.shape[0]
qp1 = Ap1.shape[0]
K = sp.zeros((Dm1, Dm1), dtype=A.dtype)
Hr = sp.zeros_like(K)
for s in xrange(q):
Ash = A[s].conj().T
for t in xrange(qp1):
test = Ap1[t]
Hr += C[t, s].dot(rp1.dot(mm.H(test).dot(Ash)))
K += A[s].dot(Kp1.dot(Ash))
op_expect = mm.adot(lm1, Hr)
K += Hr
return K, op_expect
def _calc_B_r_diss(self, op, K, C, n, set_eta=True):
if self.q[n] * self.D[n] - self.D[n - 1] > 0:
l_sqrt, l_sqrt_inv, r_sqrt, r_sqrt_inv = tm.calc_l_r_roots(
self.l[n - 1],
self.r[n],
sanity_checks=self.sanity_checks,
sc_data=("site", n))
Vsh = tm.calc_Vsh(self.A[n],
r_sqrt,
sanity_checks=self.sanity_checks)
x = self.calc_x(n, Vsh, l_sqrt, r_sqrt, l_sqrt_inv, r_sqrt_inv)
if set_eta:
self.eta[n] = sp.sqrt(mm.adot(x, x))
B = sp.empty_like(self.A[n])
for s in xrange(self.q[n]):
B[s] = mm.mmul(l_sqrt_inv, x, mm.H(Vsh[s]), r_sqrt_inv)
return B
else:
return None