Dynamic finite-size scaling after a quench at quantum transitions

TL;DR

This paper develops a comprehensive dynamic finite-size scaling theory for quantum systems after a sudden quench, applicable to both continuous and first-order quantum transitions, supported by numerical evidence in the quantum Ising ring.

Contribution

It introduces a unified scaling framework for quantum dynamics post-quench at different types of quantum transitions, including new universal behaviors at first-order transitions.

Findings

Scaling laws governed by critical exponents for continuous transitions

Universal scaling behavior controlled by energy gap at first-order transitions

Numerical validation using the quantum Ising ring model

Abstract

We present a general dynamic finite-size scaling theory for the quantum dynamics after an abrupt quench, at both continuous and first-order quantum transitions. For continuous transitions, the scaling laws are naturally ruled by the critical exponents and the renormalization-group dimension of the perturbation at the transition. In the case of first-order transitions, it is possible to recover a universal scaling behavior, which is controlled by the size behavior of the energy gap between the lowest energy levels. We discuss these findings in the framework of the paradigmatic quantum Ising ring, and support the dynamic scaling laws by numerical evidence.