# A machine learning approach to dynamical properties of quantum many-body systems

## TL;DR

This paper introduces a variational method using restricted Boltzmann machines to compute dynamical properties and spectral functions of quantum many-body systems, addressing challenges in excited state analysis.

## Contribution

It presents a novel approach combining RBMs, natural gradient descent, and Monte Carlo techniques to calculate dynamical spectra, improving accuracy and generality.

## Key findings

- Successfully computed the dynamical spin structure factor of the 1D J1-J2 Heisenberg model.
- Demonstrated improved accuracy with regularization strategies.
- Method is adaptable to various variational forms.

## Abstract

Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional $J_1-J_2$ Heisenberg model. The method is general and can be extended to other variational forms.