Probing ground-state phase transitions through quench dynamics

TL;DR

This paper demonstrates that quench dynamics can be used to probe quantum phase transitions in integrable and nearly integrable systems, providing a practical method for experimental detection of critical points.

Contribution

It introduces a finite-time scaling method to identify quantum critical points through quench dynamics in systems like the transverse-field Ising model.

Findings

Discovery of a dynamical critical point with non-analytic correlator signatures.

The dynamical critical point coincides with the quantum critical point.

Method applicable to experiments with finite time and system size.

Abstract

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.