Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions
Na Li, Yang Zhao, Wen-Long Ma, Z. D. Wang, Yan-Kui Bai
TL;DR
The paper investigates how long-range interactions shape the distribution of bipartite entanglement in the XXZ spin chain, comparing exponential and power-law decay regimes. Using DMRG methods (iDMRG for the infinite system and fDMRG for finite chains), it derives precise LBE relations: in infinite chains with ELRIs, two-spin entanglement decays exponentially and the total LBE satisfies $C^{(∞)} ∼ ξ τ^{(∞)}$ with $τ^{(∞)} ∼ C_1(rho_{i,i+1}) ∼ 1/ξ$, highlighting an entanglement truncation length that governs correlations and phase transitions. In finite chains with PLRIs, the LBE decays algebraically and the distribution can be piecewise, depending on decay mode and strength, providing a generalized view beyond the Koashi-Buzek-Imoto bound. The results generalize known LBE scaling to a prototypical long-range model and may inform quantum information tasks that exploit long-range entanglement.
Abstract
Long-range bipartite entanglement (LBE) and its distribution properties are studied in XXZ spin chains with the exponential and power-law long-range interactions (ELRIs and PLRIs). LBE quantified by two-qubit concurrence decays exponentially along with two-site distance in the infinite chain with ELRIs in the thermodynamic limit, and the long-range behavior of two-spin entanglement can detect the quantum phase transition and identify different quantum phases away from the critical point. Moreover, a fine-grained LBE distribution relation is obtained for the infinite XXZ spin chain. On the other hand, in the finite XXZ spin chain with the conventional PLRIs, the long-range concurrence decays algebraically and the total one is no longer monotonic along with the chain length. The total LBE distribution property can exhibit a piecewise function, which has a close relationship with the decaying mode and strength of PLRIs. These LBE relations can be regarded as the generalization of Koashi-Bužek-Imoto bound for the prototypical long-range XXZ model, having potential applications in quantum information processing.