def calc_x(self,
n,
Vsh,
sqrt_l,
sqrt_r,
sqrt_l_inv,
sqrt_r_inv,
right=True):
"""Calculate the parameter matrix x* giving the desired B.
This is equivalent to eqn. (49) of arXiv:1103.0936v2 [cond-mat.str-el] except
that, here, norm-preservation is not enforced, such that the optimal
parameter matrices x*_n (for the parametrization of B) are given by the
derivative w.r.t. x_n of <Phi[B, A]|Ĥ|Psi[A]>, rather than
<Phi[B, A]|Ĥ - H|Psi[A]> (with H = <Psi|Ĥ|Psi>).
Direct dependencies:
- A[n - 1], A[n], A[n + 1]
- r[n], r[n + 1], l[n - 2], l[n - 1]
- C[n], C[n - 1]
- K[n + 1]
- V[n]
"""
if n > 0:
lm2 = self.get_l(n - 2)
else:
lm2 = None
if n < self.N + 1:
C = self.C[n]
else:
C = None
if right:
x = tm.calc_x(self.K[n + 1], C, self.C[n - 1], self.r[n + 1], lm2,
self.get_A(n - 1), self.A[n], self.get_A(n + 1),
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
else:
x = tm.calc_x_l(self.K_l[n - 1], C, self.C[n - 1],
self.r[n + 1], lm2, self.get_A(n - 1), self.A[n],
self.get_A(n + 1), sqrt_l, sqrt_l_inv, sqrt_r,
sqrt_r_inv, Vsh)
return x
def calc_x(self, n, Vsh, sqrt_l, sqrt_r, sqrt_l_inv, sqrt_r_inv, right=True):
"""Calculate the parameter matrix x* giving the desired B.
This is equivalent to eqn. (49) of arXiv:1103.0936v2 [cond-mat.str-el] except
that, here, norm-preservation is not enforced, such that the optimal
parameter matrices x*_n (for the parametrization of B) are given by the
derivative w.r.t. x_n of <Phi[B, A]|Ĥ|Psi[A]>, rather than
<Phi[B, A]|Ĥ - H|Psi[A]> (with H = <Psi|Ĥ|Psi>).
Direct dependencies:
- A[n - 1], A[n], A[n + 1]
- r[n], r[n + 1], l[n - 2], l[n - 1]
- C[n], C[n - 1]
- K[n + 1]
- V[n]
"""
if n > 0:
lm2 = self.get_l(n - 2)
else:
lm2 = None
if n < self.N + 1:
C = self.C[n]
else:
C = None
if right:
x = tm.calc_x(self.K[n + 1], C, self.C[n - 1], self.r[n + 1],
lm2, self.A[n - 1], self.A[n], self.A[n + 1],
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
else:
x = tm.calc_x_l(self.K_l[n - 1], C, self.C[n - 1], self.r[n + 1],
lm2, self.A[n - 1], self.A[n], self.A[n + 1],
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
return x
def calc_x(self, n, Vsh, sqrt_l, sqrt_r, sqrt_l_inv, sqrt_r_inv):
"""Calculates the matrix x* that results in the TDVP tangent vector B.
This is equivalent to eqn. (49) of arXiv:1103.0936v2 [cond-mat.str-el] except
that, here, norm-preservation is not enforced, such that the optimal
parameter matrices x*_n (for the parametrization of B) are given by the
derivative w.r.t. x_n of <Phi[B, A]|Ĥ|Psi[A]>, rather than
<Phi[B, A]|Ĥ - H|Psi[A]> (with H = <Psi|Ĥ|Psi>).
An additional sum was added for the single-site hamiltonian.
Some multiplications have been pulled outside of the sums for efficiency.
Direct dependencies:
- A[n - 1], A[n], A[n + 1]
- r[n], r[n + 1], l[n - 2], l[n - 1]
- C[n], C[n - 1]
- K[n + 1]
- V[n]
"""
if n > 1:
lm2 = self.l[n - 2]
Cm1 = self.C[n - 1]
Am1 = self.A[n - 1]
else:
lm2 = None
Cm1 = None
Am1 = None
if n > 2:
lm3 = self.l[n - 3]
Cm2 = self.C[n - 2]
Am2Am1 = self.AA[n - 2]
else:
lm3 = None
Cm2 = None
Am2Am1 = None
if n <= self.N - self.ham_sites + 1:
C = self.C[n]
else:
C = None
if n + 1 <= self.N - self.ham_sites + 1:
Kp1 = self.K[n + 1]
else:
Kp1 = None
if n < self.N - 1:
Ap1Ap2 = self.AA[n + 1]
rp2 = self.r[n + 2]
else:
Ap1Ap2 = None
rp2 = None
if n < self.N:
rp1 = self.r[n + 1]
Ap1 = self.A[n + 1]
else:
rp1 = None
Ap1 = None
if self.ham_sites == 2:
x = tm.calc_x(Kp1, C, Cm1, rp1,
lm2, Am1, self.A[n], Ap1,
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
else:
x = tm.calc_x_3s(Kp1, C, Cm1, Cm2, rp1, rp2, lm2,
lm3, Am2Am1, Am1, self.A[n], Ap1, Ap1Ap2,
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
return x
def calc_x(self, n, Vsh, sqrt_l, sqrt_r, sqrt_l_inv, sqrt_r_inv):
"""Calculates the matrix x* that results in the TDVP tangent vector B.
This is equivalent to eqn. (49) of arXiv:1103.0936v2 [cond-mat.str-el] except
that, here, norm-preservation is not enforced, such that the optimal
parameter matrices x*_n (for the parametrization of B) are given by the
derivative w.r.t. x_n of <Phi[B, A]|Ĥ|Psi[A]>, rather than
<Phi[B, A]|Ĥ - H|Psi[A]> (with H = <Psi|Ĥ|Psi>).
An additional sum was added for the single-site hamiltonian.
Some multiplications have been pulled outside of the sums for efficiency.
Direct dependencies:
- A[n - 1], A[n], A[n + 1]
- r[n], r[n + 1], l[n - 2], l[n - 1]
- C[n], C[n - 1]
- K[n + 1]
- V[n]
"""
if n > 1:
lm2 = self.l[n - 2]
Cm1 = self.C[n - 1]
Am1 = self.A[n - 1]
else:
lm2 = None
Cm1 = None
Am1 = None
if n > 2:
lm3 = self.l[n - 3]
Cm2 = self.C[n - 2]
Am2 = self.A[n - 2]
else:
lm3 = None
Cm2 = None
Am2 = None
if n <= self.N - self.ham_sites + 1:
C = self.C[n]
else:
C = None
if n + 1 <= self.N - self.ham_sites + 1:
Kp1 = self.K[n + 1]
else:
Kp1 = None
if n < self.N - 1:
Ap2 = self.A[n + 2]
rp2 = self.r[n + 2]
else:
Ap2 = None
rp2 = None
if n < self.N:
rp1 = self.r[n + 1]
Ap1 = self.A[n + 1]
else:
rp1 = None
Ap1 = None
if self.ham_sites == 2:
x = tm.calc_x(Kp1, C, Cm1, rp1,
lm2, Am1, self.A[n], Ap1,
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
else:
x = tm.calc_x_3s(Kp1, C, Cm1, Cm2, rp1, rp2, lm2,
lm3, Am2, Am1, self.A[n], Ap1, Ap2,
sqrt_l, sqrt_l_inv, sqrt_r, sqrt_r_inv, Vsh)
return x
