Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space

TL;DR

This paper introduces a time-dependent variational Monte Carlo method for continuous-space Bose gases, enabling precise studies of ground-state properties and out-of-equilibrium dynamics, including large systems and complex quenches.

Contribution

The paper presents a novel variational Monte Carlo approach that is essentially exact and scalable, allowing detailed analysis of strongly-interacting Bose gases in continuous space.

Findings

High-precision ground-state property calculations

Accurate out-of-equilibrium dynamics after quantum quenches

Feasibility of studying large particle systems and complex protocols

Abstract

We introduce time-dependent variational Monte Carlo for continuous-space Bose gases. Our approach is based on the systematic expansion of the many-body wave-function in terms of multi-body correlations and is essentially exact up to adaptive truncation. The method is benchmarked by comparison to exact Bethe-ansatz or existing numerical results for the integrable Lieb-Liniger model. We first show that the many-body wave-function achieves high precision for ground-state properties, including energy and first-order as well as second-order correlation functions. Then, we study the out-of-equilibrium, unitary dynamics induced by a quantum quench in the interaction strength. Our time-dependent variational Monte Carlo results are benchmarked by comparison to exact Bethe ansatz results available for a small number of particles, and also compared to quench action results available for non-interacting initial states. Moreover, our approach allows us to study large particle numbers and general quench protocols, previously inaccessible beyond the mean-field level. Our results suggest that it is possible to find correlated initial states for which the long-term dynamics of local density fluctuations is close to the predictions of a simple Boltzmann ensemble.