Bound energy, entanglement and identifying critical points in 1D long-range Kitaev model

TL;DR

This paper explores the relationship between bound energy and entanglement in the long-range Kitaev model, revealing how bound energy signals critical points and breaks conformal symmetry for certain interaction decay rates.

Contribution

It analytically links bound energy to entanglement entropy and demonstrates bound energy's role in identifying critical points in a long-range quantum system.

Findings

Bound energy is proportional to the square of entanglement entropy at =1.

Bound energy exhibits a minimum at the critical point =1.

The study reveals how bound energy can detect phase transitions in long-range models.

Abstract

We investigate the entanglement structure of a bipartite quantum system through the lens of quantum thermodynamics in the absence of conformal symmetry. Specifically, we consider the long-range Kitaev model, where the pairing interaction decays as a power law with exponent $\alpha$, with broken conformal symmetry for $\alpha<3/2$. We analytically show that the bound energy, a quantum thermodynamical quantity, is linearly proportional to the square of entanglement entropy per unit system size for $\alpha=1$ where conformal symmetry is broken. We further show that for all values of $\alpha$, bound energy, in the thermodynamic limit, shows a pronounced minimum at the critical point, which enables the identification of $\mu=1$.