def ExpmbH(H_,psi_,db): phi = psi_.copy() chi = psi_.copy() i = 0 while(LA.norm(chi)>1e-6): chi = (-db/float(i+1))*Hpsi(H_,chi) phi += chi.copy() i += 1 nu = LA.norm(phi) return phi.copy()/nu,nu
def RTE(H_, dT, Tmax, lanczos=False, psi0=None):
# --- diagonalization ---
N = H_[0][2].shape[1]
nbit = int(np.log2(N))
hdiag = np.zeros(N, dtype=complex)
ei = np.zeros(N, dtype=complex)
for i in range(N):
xi = Int2Bas(i, 2, nbit)
for (A, h, imp, gmp) in H_:
nact = len(A)
for m in np.where(np.abs(h) > 1e-8)[0]:
sm = Int2Bas(m, 4, nact)
#print A,sm,[xi[A[i]] for i in range(nact)]
smx = [
sigma_matrices[xi[A[w]], xi[A[w]], sm[w]]
for w in range(nact)
]
hdiag[i] += h[m] * np.prod(smx)
if (i % 1000 == 0): print i, N, hdiag[i]
precond = lambda x, e, *args: x / (hdiag - e + 1e-4)
def hop(c_):
return Hpsi(H_, c_)
epsm0, Um0 = davidson(hop, psi0, precond)
fout = open('RTE_davidson.out', 'w')
fout.write("gs energy %.6f \n" % epsm0)
# --- initial state ---
if (psi0 is None):
i0 = np.argmin(hdiag)
psi0 = np.zeros(N, dtype=complex)
psi0[i0] = 1.0
# --- real-time evolution ---
bra_RTE = psi0[:]
braH_RTE = Hpsi(H_, psi0[:])[:]
ket_RTE = psi0[:]
nbeta = int(Tmax / dT) + 1
hvect_LANZ = np.zeros(nbeta + 1, dtype=complex)
svect_LANZ = np.zeros(nbeta + 1, dtype=complex)
fout.write("ITE\n")
for ib in range(nbeta):
hvect_LANZ[ib] = np.einsum('a,a', np.conj(braH_RTE), ket_RTE)
svect_LANZ[ib] = np.einsum('a,a', np.conj(bra_RTE), ket_RTE)
ket_RTE = ExpitH(H_, ket_RTE, dT)[0]
print ib, hvect_LANZ[ib]
dump_lanz_rte(hvect_LANZ[:nbeta], svect_LANZ[:nbeta], 'qlanz.vecs')
fout.close()
def hop(c_): return Hpsi(H_,c_)