Machine Learning out of equilibrium correlations in the Bose-Hubbard model

TL;DR

This paper develops a neural network approach to improve the accuracy of out-of-equilibrium correlation calculations in the Bose-Hubbard model, surpassing existing approximate methods and applicable to other quantum systems.

Contribution

It introduces a neural network trained on 2PISC outputs to enhance correlation amplitude predictions in the Bose-Hubbard model, extending beyond traditional approximation limits.

Findings

Neural network predictions outperform 2PISC in correlation amplitude accuracy.

The approach generalizes to parameters outside the training set.

Method aligns well with exact results and experiments in certain regimes.

Abstract

Calculating the out-of-equilibrium dynamics of many-body quantum systems theoretically is a challenging problem. Essentially exact results can be obtained for the out-of-equilibrium correlations in the Bose-Hubbard model in one dimension, but higher dimensions require approximate methods. One such method is the two-particle irreducible strong coupling (2PISC) approach [M.R.C. Fitzpatrick and M.P. Kennett, Nucl. Phys. B 930, 1 (2018)]. Calculations of the single-particle correlations using this method yield values of the velocity for correlation spreading that match well with exact methods in one dimension and experiments in one and two dimensions. However, the 2PISC method is less accurate for determining the amplitude of correlations, especially in the regime where interactions are not very strong. Viewing the calculation of the single-particle correlations as an image correction problem, we train a neural network (NN) to take input from the 2PISC approach to reproduce the output of exact diagonalization calculations. We show that the predictions of the NN improve on 2PISC results for parameters outside the training region. Our approach is not specific to the Bose-Hubbard model and may find application to the out-of-equilibrium dynamics of other quantum many-body systems.