Microscopic theory of non-adiabatic response in real and imaginary time

TL;DR

This paper develops a unified framework for analyzing non-adiabatic dynamics in quantum systems in both real and imaginary time, connecting response functions, critical point detection, and quantum Monte Carlo methods.

Contribution

It introduces a general approach linking real and imaginary time evolution, enabling extraction of geometric quantities and critical point detection in quantum systems.

Findings

Real and imaginary time evolutions show strong qualitative and quantitative similarities.

Scaling theory effectively detects quantum critical points in quenched systems.

Recent quantum Monte Carlo methods are reviewed for imaginary-time evolution studies.

Abstract

We present a general approach to describe slowly driven quantum systems both in real and imaginary time. We highlight many similarities, qualitative and quantitative, between real and imaginary time evolution. We discuss how the metric tensor and the Berry curvature can be extracted from both real and imaginary time simulations as a response of physical observables. For quenches ending at or near the quantum critical point, we show the utility of the scaling theory for detecting the location of the quantum critical point by comparing sweeps at different velocities. We briefly discuss the universal relaxation to equilibrium of systems after a quench. We finally review recent developments of quantum Monte Carlo methods for studying imaginary-time evolution. We illustrate our findings with explicit calculations using the transverse field Ising model in one dimension.