Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

TL;DR

This paper investigates how avoided crossings near excited-state quantum phase transitions in the Lipkin-Meshkov-Glick model lead to increased delocalization and dynamical tunneling, using the Wherl entropy as a key tool.

Contribution

It introduces the use of Wherl entropy to detect superpositions of classical trajectories and analyze dynamical tunneling near ESQPTs in the Lipkin-Meshkov-Glick model.

Findings

Sudden increase in Wherl entropy near critical energy

Detection of superpositions of classical trajectories in eigenstates

Enhanced dynamical tunneling observed in evolved states

Abstract

Using the Wherl entropy, we study the delocalization in phase-space of energy eigenstates in the vicinity of avoided crossing in the Lipkin-Meshkov-Glick model. These avoided crossing, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase space regions, which contrary to the low energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wherl entropy is observed for eigenstates close to the critical energy of the excited-state quantum phase transition (ESQPT). This allows to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi functions of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.