def ph_onsite(cls, mol_list: MolList, opera: str, mol_idx:int, ph_idx=0):
assert opera in ["b", r"b^\dagger", r"b^\dagger b"]
mpo = cls()
mpo.mol_list = mol_list
for imol, mol in enumerate(mol_list):
if mol_list.scheme < 4:
mpo.append(xp.eye(2).reshape(1, 2, 2, 1))
elif mol_list.scheme == 4:
if len(mpo) == mol_list.e_idx():
n = mol_list.mol_num
mpo.append(xp.eye(n).reshape(1, n, n, 1))
else:
assert False
iph = 0
for ph in mol.dmrg_phs:
for iqph in range(ph.nqboson):
ph_pbond = ph.pbond[iqph]
if imol == mol_idx and iph == ph_idx:
mt = ph_op_matrix(opera, ph_pbond)
else:
mt = ph_op_matrix("Iden", ph_pbond)
mpo.append(mt.reshape(1, ph_pbond, ph_pbond, 1))
iph += 1
mpo.build_empty_qn()
return mpo
def exact_propagator(cls, mol_list: MolList, x, space="GS", shift=0.0):
"""
construct the GS space propagator e^{xH} exact MPO
H=\\sum_{in} \\omega_{in} b^\\dagger_{in} b_{in}
fortunately, the H is local. so e^{xH} = e^{xh1}e^{xh2}...e^{xhn}
the bond dimension is 1
shift is the a constant for H+shift
"""
assert space in ["GS", "EX"]
mpo = cls()
if np.iscomplex(x):
mpo.to_complex(inplace=True)
mpo.mol_list = mol_list
for imol, mol in enumerate(mol_list):
if mol_list.scheme < 4:
mo = np.eye(2).reshape(1, 2, 2, 1)
mpo.append(mo)
elif mol_list.scheme == 4:
if len(mpo) == mol_list.e_idx():
n = mol_list.mol_num
mpo.append(np.eye(n).reshape(1, n, n, 1))
else:
assert False
for ph in mol.dmrg_phs:
if space == "EX":
# for the EX space, with quasiboson algorithm, the b^\dagger + b
# operator is not local anymore.
assert ph.nqboson == 1
ph_pbond = ph.pbond[0]
# construct the matrix exponential by diagonalize the matrix first
phop = construct_ph_op_dict(ph_pbond)
h_mo = (
phop[r"b^\dagger b"] * ph.omega[0]
+ phop[r"(b^\dagger + b)^3"] * ph.term30
+ phop[r"b^\dagger + b"] * (ph.term10 + ph.term11)
+ phop[r"(b^\dagger + b)^2"] * (ph.term20 + ph.term21)
+ phop[r"(b^\dagger + b)^3"] * (ph.term31 - ph.term30)
)
w, v = scipy.linalg.eigh(h_mo)
h_mo = np.diag(np.exp(x * w))
h_mo = v.dot(h_mo)
h_mo = h_mo.dot(v.T)
mo = h_mo.reshape(1, ph_pbond, ph_pbond, 1)
mpo.append(mo)
elif space == "GS":
anharmo = False
# for the ground state space, yet doesn't support 3rd force
# potential quasiboson algorithm
ph_pbond = ph.pbond[0]
for i in range(len(ph.force3rd)):
anharmo = not np.allclose(
ph.force3rd[i] * ph.dis[i] / ph.omega[i], 0.0
)
if anharmo:
break
if not anharmo:
for iboson in range(ph.nqboson):
d = np.exp(
x
* ph.omega[0]
* ph.base ** (ph.nqboson - iboson - 1)
* np.arange(ph_pbond)
)
mo = np.diag(d).reshape(1, ph_pbond, ph_pbond, 1)
mpo.append(mo)
else:
assert ph.nqboson == 1
# construct the matrix exponential by diagonalize the matrix first
phop = construct_ph_op_dict(ph_pbond)
h_mo = (
phop[r"b^\dagger b"] * ph.omega[0]
+ phop[r"(b^\dagger + b)^3"] * ph.term30
)
w, v = scipy.linalg.eigh(h_mo)
h_mo = np.diag(np.exp(x * w))
h_mo = v.dot(h_mo)
h_mo = h_mo.dot(v.T)
mo = np.zeros([1, ph_pbond, ph_pbond, 1])
mo[0, :, :, 0] = h_mo
mpo.append(mo)
else:
assert False
# shift the H by plus a constant
mpo.qn = [[0]] * (len(mpo) + 1)
mpo.qnidx = len(mpo) - 1
mpo.qntot = 0
# np.exp(shift * x) is usually very large
mpo = mpo.scale(np.exp(shift * x), inplace=True)
return mpo
