Chebyshev expansion of spectral functions using restricted Boltzmann machines

TL;DR

This paper introduces a novel variational method combining Chebyshev expansion and neural networks to compute spectral functions in 2D quantum systems, overcoming traditional computational challenges.

Contribution

It presents a new approach that uses neural networks and Chebyshev moments to efficiently calculate spectral functions in two-dimensional systems.

Findings

Effective in 2D Heisenberg models

Comparable accuracy to existing methods

Addresses sign problem and entanglement challenges

Abstract

Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional systems present insurmountable hurdles, ranging from the sign problem in quantum Monte Carlo (MC), to the entanglement area law in tensor network based methods. We hereby present a variational approach based on a Chebyshev expansion of the spectral function and a neural network representation for the wave functions. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave-functions". We present results for the one-dimensional and two-dimensional Heisenberg model on the square lattice, and compare to those obtained by other methods in the literature.