Linear-response approach to critical quantum many-body systems

TL;DR

This paper introduces a practical method combining finite-size scaling and linear response to efficiently identify energy gaps and critical exponents in quantum many-body systems, applicable to both integrable and non-integrable models.

Contribution

A novel, experimentally feasible scheme that infers critical properties of quantum systems from excited states without requiring ground state preparation.

Findings

Successfully extracts energy gaps in various models

Applicable to both integrable and non-integrable systems

Operates without ground state preparation

Abstract

The characterization of quantum critical phenomena is pivotal for the understanding and harnessing of quantum many-body physics. However, their complexity makes the inference of such fundamental processes difficult. Thus, efficient and experimentally non-demanding methods for their diagnosis are strongly desired. Here, we introduce a general scheme, based on the combination of finite-size scaling and the linear response of a given observable to a time-dependent perturbation, to efficiently extract the energy gaps to the lowest excited states of the system, and thus infer its dynamical critical exponents. Remarkably, the scheme is able to tackle both integrable and non-integrable models, prepared away from their ground states. It thus holds the potential to embody a valuable diagnostic tool for experimentally significant problems in quantum many-body physics.