Chiral Topological Phases from Artificial Neural Networks

TL;DR

This paper explores the use of artificial neural networks, specifically restricted Boltzmann machines, to efficiently model and analyze chiral topological phases like fractional quantum Hall states, achieving accurate approximations and explicit constructions.

Contribution

It demonstrates that ANNs can effectively approximate FQH states and explicitly constructs the Laughlin wave-function as an ANN state, revealing new computational approaches.

Findings

ANNs can approximate FQH states with good accuracy

Explicit construction of Laughlin wave-function as an ANN state

ANN wave-functions can exactly represent n-body correlations

Abstract

Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate as to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how n-body correlations can be kept at an exact level with ANN wave-functions exhibiting polynomial scaling with power n in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave-function as an ANN state.