def example_exact_diagonalization(L, Jz):
xxz_pars = dict(L=L, Jxx=1., Jz=Jz, hz=0.0, bc_MPS='finite')
M = XXZChain(xxz_pars)
product_state = ["up", "down"] * (xxz_pars['L'] // 2) # this selects a charge sector!
psi_DMRG = MPS.from_product_state(M.lat.mps_sites(), product_state)
charge_sector = psi_DMRG.get_total_charge(True) # ED charge sector should match
ED = ExactDiag(M, charge_sector=charge_sector, max_size=2.e6)
ED.build_full_H_from_mpo()
# ED.build_full_H_from_bonds() # whatever you prefer
print("start diagonalization")
ED.full_diagonalization() # the expensive part for large L
E0_ED, psi_ED = ED.groundstate() # return the ground state
print("psi_ED =", psi_ED)
print("run DMRG")
dmrg.run(psi_DMRG, M, {'verbose': 0}) # modifies psi_DMRG in place!
# first way to compare ED with DMRG: convert MPS to ED vector
psi_DMRG_full = ED.mps_to_full(psi_DMRG)
print("psi_DMRG_full =", psi_DMRG_full)
ov = npc.inner(psi_ED, psi_DMRG_full, axes='range', do_conj=True)
print("<psi_ED|psi_DMRG_full> =", ov)
assert (abs(abs(ov) - 1.) < 1.e-13)
# second way: convert ED vector to MPS
psi_ED_mps = ED.full_to_mps(psi_ED)
ov2 = psi_ED_mps.overlap(psi_DMRG)
print("<psi_ED_mps|psi_DMRG> =", ov2)
assert (abs(abs(ov2) - 1.) < 1.e-13)
assert (abs(ov - ov2) < 1.e-13)
# -> advantage: expectation_value etc. of MPS are available!
print("<Sz> =", psi_ED_mps.expectation_value('Sz'))
xxz_pars = dict(L=4, Jxx=1., Jz=1., hz=0.0, bc_MPS='finite')
M = XXZChain(xxz_pars)
ED = ExactDiag(M, [0])
ED.build_full_H_from_mpo()
# ED.build_full_H_from_bonds() # whatever you prefer
print("start diagonalization")
ED.full_diagonalization()
psi_ED = ED.groundstate()
print("psi_ED =", psi_ED)
print("start DMRG")
product_state = [0, 1] * (xxz_pars['L'] // 2) # this selects a charge sector!
psi_DMRG = MPS.from_product_state(M.lat.mps_sites(), product_state)
res = run_DMRG(psi_DMRG, M, {'verbose': 0})
# first way to compare ED with DMRG: convert MPS to ED vector
psi_DMRG_full = ED.mps_to_full(psi_DMRG)
print("psi_DMRG_full =", psi_DMRG_full)
ov = abs(npc.inner(psi_ED, psi_DMRG_full, do_conj=True))
print("|<psi_ED|psi_DMRG>| =", ov)
assert (abs(ov - 1.) < 1.e-13)
# second way: convert ED vector to MPS
psi_ED_mps = ED.full_to_mps(psi_ED)
ov = psi_ED_mps.overlap(psi_DMRG)
print("|<psi_ED_mps|psi_DMRG>| =", abs(ov))
assert (abs(abs(ov) - 1.) < 1.e-13)
# -> advantange: expectation_value etc. of MPS are available!
print("<Sz> =", psi_ED_mps.expectation_value('Sz'))