Universal nonequilibrium quantum dynamics in imaginary time

TL;DR

This paper introduces a universal method to analyze quantum dynamics in imaginary time, revealing non-adiabatic responses at quantum-critical points and extending finite-size scaling to non-equilibrium scenarios, with practical QMC simulation techniques.

Contribution

It presents a novel imaginary-time evolution approach for quantum systems, connecting non-adiabatic responses to universal exponents and developing a QMC scheme for non-equilibrium quantum dynamics.

Findings

Universal non-adiabatic response characterized by critical exponents.

Finite-size scaling extended to non-equilibrium imaginary-time dynamics.

QMC simulations successfully applied to quantum-critical quenches in 1D and 2D.

Abstract

We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and characterized by the same exponents in real and imaginary time. For a linear quench protocol, the fidelity susceptibility and the geometric tensor naturally emerge in the response functions. Beyond linear response, we extend the finite-size scaling theory of quantum phase transitions to non-equilibrium setups. This allows, e.g., for studies of quantum phase transitions in systems of fixed finite size by monitoring expectation values as a function of the quench velocity. Non-equilibrium imaginary-time dynamics is also amenable to quantum Monte Carlo (QMC) simulations, with a scheme that we introduce here and apply to quenches of the transverse-field Ising model to quantum-critical points in one and two dimensions. The QMC method is generic and can be applied to a wide range of models and non-equilibrium setups.