Quantum correlations in critical $XXZ$ system and LMG model

TL;DR

This paper studies quantum phase transitions in the $XXZ$ spin chain and LMG model using various quantum correlation measures, revealing their effectiveness in detecting critical points.

Contribution

It provides a comparative analysis of quantum correlations in $XXZ$ and LMG models, highlighting which measures signal phase transitions at specific points.

Findings

All correlations detect transition at Δ=-1

Information deficit and local quantum uncertainty detect transition at Δ=1

Analytical and numerical analysis of quantum correlations

Abstract

We investigate the quantum phase transitions for the $XXZ$ spin-1/2 chains via the quantum correlations between the nearest and next to nearest neighbor spins characterized by negativity, information deficit, trace distance discord and local quantum uncertainty. It is shown that all these correlations exhibit the quantum phase transitions at $\Delta=-1$. However, only information deficit and local quantum uncertainty can demonstrate quantum phase transitions at $\Delta=1$. The analytical and numerical behaviors of the quantum correlations for the $XXZ$ system are presented. We also consider quantum correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick (LMG) model.