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arXiv · 2112.06648

Impact of chaos on precursors of quantum criticality

Ignacio García-Mata·Diego A. Wisniacki·Eduardo G. Vergini
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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}

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Ignacio García-Mata, Diego A. Wisniacki, Eduardo G. Vergini. 2021-12-06. Impact of chaos on precursors of quantum criticality. https://doi.org/10.1103/physreve.104.l062202

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