Excited-state quantum phase transition and the quantum speed limit

TL;DR

This paper explores how an excited-state quantum phase transition (ESQPT) affects the quantum speed limit (QSL) time in an open quantum system, revealing a slowdown at the ESQPT critical point linked to decoherence rate singularities.

Contribution

It demonstrates the impact of ESQPT on QSL time and uncovers the mechanism behind the slowdown, independent of environment Markovianity.

Findings

QSL time peaks sharply at ESQPT critical energy

Qubit decoherence rate exhibits singular behavior at ESQPT

Slowdown occurs regardless of environment Markovianity

Abstract

We investigate the influence of an excited-state quantum phase transition (ESQPT) on the quantum speed limit (QSL) time of an open quantum system. The system consists of a central qubit coupled to a spin environment modeled by a Lipkin-Meshkov-Glick (LMG) Hamiltonian. We show that when the coupling between qubit and environment is such that the latter is located at the ESQPT critical energy the qubit evolution shows a remarkable slowdown, marked by an abrupt peak in the QSL time. Interestingly, this slowdown at the ESQPT critical point is induced by the singular behavior of the qubit decoherence rate, being independent of the Markovian nature of the environment.