Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model

TL;DR

This paper investigates how genuine multipartite correlations behave in the Lipkin-Meshkov-Glick model, revealing their role in signaling quantum phase transitions and determining critical exponents through finite-size scaling.

Contribution

It provides a detailed analysis of genuine multipartite correlations of all orders in the LMG model, highlighting their significance in quantum criticality.

Findings

GMC of all orders signals the second order quantum phase transition.

Finite-size scaling yields critical exponents for certain correlation orders.

GMC distribution offers insights beyond bipartite correlations in critical phenomena.

Abstract

Correlations play a key role in critical phenomena. Quantities such as the entanglement entropy, for instance, provide key insights into the mechanisms underlying quantum criticality. Almost all of our present knowledge, however, is restricted to bipartite correlations. Some questions still remain unanswered, such as: What parcel of the total correlations are genuinely k-partite? With the goal of shedding light on this difficult question, in this paper we put forth a detailed study of the behavior of genuine multipartite correlations (GMC) of arbitrary orders in the Lipkin-Meshkov-Glick model. We find that GMC of all orders serve to signal the second order quantum phase transition presented in the model. Applying finite-size scaling methods, we also find the critical exponents for some orders of correlations.