import numpy as np
import sys
sys.path.append('../../../../../code_v4/')
from hamiltonian import Heisenberg_LR, print_Hamiltonian
from mf import hom_mf_solution, hom_mf_state, hom_mf_energy, mf_solution, mf_state, mf_energy
from ite import ITE_FCI
from qite import QITE
from binary_functions import Bas2Int
nspin = 2
R = 0.50
db = 0.01
bmax = 4.00
H = Heisenberg_LR(nspin, R)
print_Hamiltonian(H)
# AFM initial guess
psi_0 = np.zeros(2**nspin, dtype=complex)
xvec = [0, 1] * (nspin / 2)
xind = Bas2Int(xvec, 2)
psi_0[xind] = 1.0
ITE_FCI(H, db, bmax, psi0=psi_0)
QITE(H, db, bmax, lanczos=False, psi0=psi_0, ncheck=10)
def QITE_step(H_, psi_, db, xv, check):
import time
nalpha = len(H_)
dn_ = 1.0
if (xv is None):
xv = []
for alpha in range(nalpha):
(A, h, imp, gmp) = H_[alpha]
nact = imp.shape[0]
xv.append(np.zeros(nact))
for alpha in range(nalpha):
# ----- target state
t0 = time.time()
delta_alpha, dnalpha_ = ExpmbH_alpha(H_, psi_, alpha, db)
delta_alpha -= psi_.copy()
dn_ *= dnalpha_
Xop = []
# ----- pauli action
(A, h, imp, gmp) = H_[alpha]
nact = imp.shape[0]
# print('active:',imp)
Pmu_psi = np.zeros(imp.shape, dtype=complex)
for m in range(nact):
Pmu_psi[m, :] = gmp[m, imp[m, :]] * psi_[imp[m, :]]
t1 = time.time()
# ----- set linear system
Amat = np.dot(np.conj(Pmu_psi), Pmu_psi.T)
# print('Amat:\n',Amat)
Amat = 2.0 * np.real(Amat)
t2 = time.time()
bvec = np.dot(Pmu_psi, np.conj(delta_alpha))
bvec = -2.0 * np.imag(bvec)
t3 = time.time()
if (check):
x = SciLA.lstsq(Amat, bvec)[0]
else:
zct = np.dot(bvec, Amat)
def cost_fun(vct):
return LA.norm(np.dot(Amat, vct) - bvec)**2
def J_cost_fun(vct):
wct = np.dot(Amat, vct)
wct = np.dot(Amat.T, wct)
return 2.0 * (wct - zct)
import scipy
x = scipy.optimize.minimize(cost_fun,
x0=xv[alpha],
method='Newton-CG',
jac=J_cost_fun,
tol=1e-8).x
xv[alpha] = x.copy()
print('Pauli Operator')
Xop.append((A, x, imp, gmp))
print_Hamiltonian(Xop)
# print_Hamiltonian(xv)
#print('\n wavefunction before\n',Pmu_psi)
t4 = time.time()
psi_ = Exp_ixP(x, psi_, imp, gmp)
#print('\n wavefunction after\n', psi_,'\n')
t5 = time.time()
# print alpha,t5-t4,t4-t3,t3-t2,t2-t1,t1-t0
import sys
sys.stdout.flush()
# print('op:\n',xv)
return psi_, dn_, xv, Xop