Bell-type correlation at quantum phase transitions in spin-1 chain

TL;DR

This paper introduces a Bell-type correlation method applied to a spin-1 chain to accurately identify various quantum phase transitions, revealing the significance of high-order terms in critical phenomena.

Contribution

It generalizes bipartite Bell correlation to include high-order terms and applies density-matrix renormalisation group to detect quantum phases in a spin-1 chain.

Findings

Bell-type correlation can identify diverse quantum phase transitions.

High-order terms play a crucial role in quantum criticality.

The method provides precise characterization of non-trivial quantum phases.

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 density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-SLK-type generalized 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 has been revealed.