Quenches near criticality of the quantum Ising chain---power and limitations of the discrete truncated Wigner approximation

TL;DR

This paper systematically benchmarks the discrete truncated Wigner approximation (dTWA) for the quantum Ising chain near criticality, revealing its limitations after quenches into the quantum critical regime and highlighting where quantum simulators outperform semi-classical methods.

Contribution

It provides a detailed assessment of dTWA's performance in one-dimensional quantum critical quenches, identifying its limitations and guiding future quantum simulation applications.

Findings

dTWA shows limitations after quenches into the quantum critical regime

Semi-classical simulations cannot capture all quantum critical dynamics

Quantum simulators can access information beyond semi-classical methods

Abstract

The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-$1/2$ systems. While it appears to provide a powerful approach which shows promising results in higher dimensions and for systems with long-range interactions, its performance is still not well understood in general. Here we perform a systematic benchmark on the one-dimensional transverse-field Ising model and point to limitations of the approximation arising after sudden quenches into the quantum critical regime. Our procedure allows to identify the limitations of the semi-classical simulations and with that to determine the regimes and questions where quantum simulators can provide information which is inaccessible to semi-classics.