The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

TL;DR

This paper investigates how weak chaos influences the accuracy of analog quantum simulations of quantum critical phenomena, showing that some global transition estimates are robust while local measurements are fragile.

Contribution

It introduces a protocol to measure quantum phase transitions in the presence of chaos and analyzes their robustness in analog quantum simulators.

Findings

Critical point estimates are robust to chaos.

Local measurements like mean magnetization are fragile.

Global phase space structures remain reliable indicators.

Abstract

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization are fragile, and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs. those that depend on local trajectories.