Multipartite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2XXZchain

Abstract

In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Belltype inequalities, we investigate multi-partite quantum nonlocality in an infinite one-dimensional quantum spin-1 2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order QPT (or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multi-partite nonlocality would be observed at the infinite-order QPT point in a Belltype experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional XY model, where multi-partite nonlocality with the highest hierarchy has been observed. Thus, multi-partite nonlocality provides us an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

“…Remarkably, a few years ago it was realized that entanglement plays a fundamental role in critical phenomena and that different measures of entanglement can be used to determine the location of several types of QPTs [9][10][11][12][13][14][15][16][17][18][19][20][21]. Furthermore, the relation of Bell inequalities and criticality has been recently explored [22][23][24].…”

Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states

“…Quantum many-body systems have been established to be a possible candidate for the implementation of quantum information protocols and powerful quantum computers [1,2,3]. with tools such as the entanglement and the QD that are realized experimentally in various setups [38,39,40]. Also, numerous studies have been extended within the scope of the non-equilibrium dynamics of QCs in many-body system.…”

Einstein–Podolsky–Rosen steering in critical systems

“…Traditionally, a QPT is described in the framework of the Landau-Ginzburg paradigm that the transition from one phase to another is usually accompanied by symmetry breaking. In recent years, many works paid attention to this problem from the quantum information perspective [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] (e.g. fidelity [16,17], quantum echo [18], quantum quench dynamics [20]).…”

“…Specifically, quantum systems possess genius nonlocal correlations, which are fundamental to varying applications of quantum information theory and technology. Since correlations among the subsystems of many-body systems are closely related to the emergence of the QPT, it is natural to investigate the link between this phenomena and nonlocal correlations [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Particularly, nonlocal correlation measures such as entanglement and Bell nonlocality have been employed to investigate QPT in numerous quantum spin systems.…”