Critical behavior of the energy gap and its relation with the Berry phase close to the excited state quantum phase transition in the Lipkin model

TL;DR

This paper investigates the relationship between the energy gap and Berry phase near excited state quantum phase transitions in the Lipkin model, revealing a linear dependence and similar critical behavior.

Contribution

It derives a relation between the energy gap and Berry phase near ESQPTs using the Hellmann-Feynman theorem, highlighting their critical behavior connection.

Findings

Energy gap linearly depends on Berry phase near ESQPT

Critical behavior of energy gap mirrors that of Berry phase

Semiclassical analysis supports the critical behavior findings

Abstract

In our previous work [Phys. Rev. A \textbf{85}, 044102 (2012)], we have studied the Berry phase of the ground state and exited states in the Lipkin model. In this paper, using Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase close to the excited state quantum phase transition (ESQPT) in the Lipkin model. We find that the energy gap is linearly dependent upon the Berry phase close to the ESQPT. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.