Impact of chaos on precursors of quantum criticality

TL;DR

This paper investigates how chaos influences the precursors of excited-state quantum phase transitions (ESQPTs), revealing that increased chaos diminishes these precursors due to interference effects, using semiclassical wave propagation theory.

Contribution

It introduces a semiclassical framework to analyze ESQPTs in quantum maps and demonstrates how chaos suppresses finite-size precursors through interference of unstable orbits.

Findings

Finite-size precursors shrink with increasing chaos

Destructive interference between homoclinic orbits explains precursor suppression

Semiclassical wave propagation effectively describes ESQPT phenomena

Abstract

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. {For systems with a classical counterpart,} these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT {for the quantum standard map: a paradigmatic example of a kicked quantum system}. {Moreover, we show that finite-size precursors of ESQPTs shrink as chaos increases due to the disturbance of the system. This phenomenon is explained through destructive interference between principal homoclinic orbits}