Bell-Type Correlation at Quantum Phase Transitions in Spin-1 Chain.

Dongkeun Lee,Wonmin Son

doi:10.3390/e22111282

Abstract

For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of the density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-type correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase have been revealed.

Highlights

Quantum correlation, that has no classical counterparts, plays a pivotal role in studying the many-body systems
We have investigated CGLMP correlations in the 1D XXZ model with onsite anisotropy especially near the quantum phase transitions
In the case of spin-1, the CGLMP correlation obtained from local measurements in the Fourier bases can be interestingly interpreted as a linear combination of the first-order and second-order transverse spin–spin correlations

Summary

Introduction

That has no classical counterparts, plays a pivotal role in studying the many-body systems. The entanglement entropy demonstrates logarithmic divergence at critical points, whereas it saturates noncritical systems associated with the area law [5,6] The localizable entanglement, another measure of entanglement, is used to detect the phase transition in spin-1/2 XXZ model and to show the divergence of the entanglement length in valence-bond solid states [7,8]. Bell correlation demonstrates the non-analyticity at the critical point while, due to the monogamy characteristics of the correlation, any bipartite Bell inequality is not violated by the translational invariant many-body systems [15] It is in two-dimensional local Hilbert space that the most Bell correlations are elucidated in aforementioned studies.

The 1d Spin-1 XXZ Model with the On-Site Anisotropy

Bell-Type Correlation from the Generalized Nonlocality Criteria

Quantum Criticality through the Correlation for the Nonlocality Tests

Conclusions