Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped t-J loop

Abstract

We investigate the ground state and excitations of finite-size Heisenberg loops doped with one hole as the simplest example to illustrate the nature of strong correlations in a doped Mott insulator. We show that the doped hole form a peculiar long-range entanglement with the surrounding spins as revealed by inspecting the mutual correlations between the charge and spin using exact diagonalization (ED). In particular, the one-hole ground state acquires a series of non-trivial total momenta depending on the ratio J/t (J and t denote the superexchange coupling and hopping integral, respectively), which gives rise to distinct quantum phases separated by critical points (CPs). Interestingly the novel total momentum and correlations completely disappear once a singular sign structure is turned off in the t-J model, indicating the latter is the true original source for strong correlation via many-body quantum interference. We emphasize that the novelties discovered here are not restricted to the one-dimensional loop. We introduce a new charge-spin mutual entanglement that can well characterize these exotic properties, which can be then easily generalized to more realistic situations like two dimensions.

Preoperative Microbiomes and Intestinal Barrier Function Can Differentiate Prodromal Alzheimer’s Disease From Normal Neurocognition in Elderly Patients Scheduled to Undergo Orthopedic Surgery

“…Lachnospiraceae_NK4A136_group was enriched in aMCI patients in our study, which was similar to the animal study ( Gao et al., 2019 ) and opposite to findings obtained in dementia patients ( Stadlbauer et al., 2020 ). Ruminococcaceae_UCG-013 , belonging to the family Ruminococcaceae , was enriched in the aMCI group compared with the SCD group in our study and was negatively correlated with inflammation and T2DM ( Wu et al., 2017 ; Wei et al., 2018 ). A high abundance of Faecalibacterium was detected in aMCI patients compared to NC patients, which was also reported in patients with chronic insomnia ( Jiang et al., 2020 ).…”

Quantum entanglement in the t−J chain: From charge-spin separation to recombination

“…However, at J/t = 0.3, where the spin-charge separation has been clearly seen in FIG. 1(a), we see that mEE clearly indicates the difference between two models not only exhibiting in ground state [14] but also persisting over to the finite-energy density. From FIG.…”

“…Such an issue has been recently addressed [14] in the study of the one-dimensional (1D) t-J model. For physical interests, the two-dimensional (2D) t-J model is considered as a "standard model" closely related to the socalled doped Mott insulator and high-temperature superconductivity in the cuprate [15][16][17][18].…”

“…We shall set the hopping integral t = 1.0 and vary the ratio J/t with noting that J/t 0.3 is commonly regarded as close to the realistic situation in the cuprate [17]. It has also been previously found [14] that in a finitesize one-hole-doped t-J ring, there are a series of distinct ground states characterized by different momenta as one tunes the ratio J/t, in contrast to a single ground states of the σ · t-J model in the whole regime of J/t. FIG.1 shows that for the t-J case, the doped hole is charge-spin separated at small J/t but recombined at larger t/J, corresponding to these distinct ground states in two limits.…”

“…We have examined two kinds of entanglement entropy, namely, the conventional von Neumann bipartite entanglement called bEE and the mutual entanglement between the charge and spin degrees of freedom called mEE introduced in Ref. [14]. Our results have clearly shown that whereas bEE fails to detect the distinct phases as a function of the ratio J/t, including the spin-charge separation as the hallmark of strong correlation in the small J/t regime of the t-J model, mEE can effectively identify all of them, not only in the ground state, but also in highly excited states of finite energy density.…”