Signature of special behaviours of $1/r^2$ interaction in the quantum entanglement entropy

TL;DR

This paper investigates how the bipartite von Neumann entropy behaves in a two-particle quantum system with a long-range $1/r^2$ interaction near a phase transition, revealing distinct behaviors in different regimes and a multicritical scaling at a specific interaction strength.

Contribution

It uncovers the different entanglement entropy behaviors across critical and first order quantum phase transitions in a $1/r^2$ interaction system and identifies a multicritical scaling behavior.

Findings

Entanglement entropy differs between critical and first order regimes.

A multicritical scaling behavior exists for $g$ in (-2, 1/4).

The transition point at $g=-3/4$ acts as a multicritical point.

Abstract

We study the bipartite von Neumann entropy of two particles interacting via a long-range scale-free potential $V(r)\sim -g/r^2$ in three dimensions, close to the unbinding transition. The nature of the quantum phase transition changes from critical ($-3/4<g<1/4$) to first order ($g<-3/4$) with $g=-3/4$ as a multicritical point. Here we show that the entanglement entropy has different behaviours for the critical and the first order regimes. But still there exists an interesting multicritical scaling behaviour for all $g\in (-2<g<1/4)$ controlled by the $g=-3/4$ case.