Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped t-J loop
Abstract: A doped Mott insulator exhibits peculiar properties associated with a singular sign structure. As a case study, we investigate the ground state and excitations of finite-size Heisenberg loops doped by one hole using exact diagonalization. We find a series of quantum critical points (QCPs) separating regimes with distinct total momenta in the axis of the ratio J/t (J and t denote the superexchange coupling and hopping integral, respectively). Each QCP involves a crystal momentum jump with level crossing or merging of the lowest energy levels. Turning off the phase-string sign structure, by contrast, we show that the total momentum of the ground state reduces to null in the whole regime of J/t with no more QCP or incoherence. We introduce the so-called charge-spin mutual entanglement to characterize these novel properties, with the entanglement spectrum providing additional information on the charge incoherence, which captures the nature of strong correlation due to the many-body quantum interference. At last, I will provide some further discussion related to sign problem and eigenstate thermalization hypothesis (ETH).