A Projector Quantum Monte Carlo Method for non-linear wavefunctions

TL;DR

This paper introduces a novel projector quantum Monte Carlo method that employs deep learning neural networks and tensor network states to efficiently optimize non-linear wavefunctions, enabling scalable solutions for strongly correlated systems.

Contribution

It reformulates the imaginary-time evolution in terms of a Lagrangian minimization, allowing polynomial complex wavefunctions and leveraging deep learning for optimization.

Findings

Successfully applied to the Hubbard model

Demonstrated application to periodic graphene sheet

Achieved scalable optimization of wavefunctions

Abstract

We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations, circumventing the exponential scaling of the approach. While previously these functions have traditionally inhabited the domain of Variational Monte Carlo, we consider recently developments for the identification of deep-learning neural networks to optimize this Lagrangian, which can be written as a modification of the propagator for the wavefunction dynamics. We demonstrate this approach with a form of Tensor Network State, and use it to find solutions to the strongly-correlated Hubbard model, as well as its application to a fully periodic ab-initio Graphene sheet. The number of variables which can be simultaneously optimized greatly exceeds alternative formulations of Variational Monte Carlo, allowing for systematic improvability of the wavefunction flexibility towards exactness for a number of different forms, whilst blurring the line between traditional Variational and Projector quantum Monte Carlo approaches.