Non-equilibrium quantum dynamics of interacting integrable models by Monte Carlo sampling Lehmann representations

TL;DR

This paper introduces a Monte Carlo sampling method to evaluate the Lehmann representation for time-dependent expectation values in interacting integrable quantum systems, enabling analysis of larger systems and longer times.

Contribution

The authors develop a novel Monte Carlo sampling scheme that efficiently computes real-time dynamics in integrable models, extending the accessible system sizes and times beyond existing methods.

Findings

Accurate benchmarking against exact results for non-interacting models.

Successful application to the Lieb-Liniger model showing evolution of the order parameter.

Identification of a sign problem in more general dynamical correlators.

Abstract

Determining the dynamics of interacting integrable many-particle quantum systems at finite times after homogeneous quantum quenches is a long-standing challenge. We present a Monte Carlo sampling scheme that numerically evaluates the Lehmann representation for time-dependent expectation values of local operators, allowing us to access system sizes and times significantly beyond the reach of existing methods. The approach accommodates both the full Lehmann sum and the Quench Action formalism. We benchmark against exact results for non-interacting lattice and continuum models and short-time results at weak interactions, finding excellent agreement. We apply the method to quantum quenches from a Bose-Einstein condensate in the repulsive Lieb-Liniger model and determine the time evolution of the order parameter for a wide range of interaction strengths. We discuss the emergence of a "sign problem" for more general dynamical correlators and setups.