Stochastically Projecting Tensor Networks

TL;DR

This paper enhances tensor network methods for quantum many-body problems by integrating projection techniques like quantum Monte Carlo and Lanczos steps, significantly improving ground state energy estimates with minimal extra computational cost.

Contribution

It introduces a novel combination of tensor networks with projection methods to improve accuracy in ground state energy calculations.

Findings

Achieved up to 57% of the remaining energy correction beyond tensor networks.

Demonstrated effectiveness on the triangular lattice Heisenberg model.

Showed minimal additional computational cost for improved accuracy.

Abstract

We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as well as tree tensor networks in this work. Building on top of these approaches, we apply fixed-node quantum Monte Carlo, Lanczos steps, and exact projection. We demonstrate these improvements for the triangular lattice Heisenberg model, where we capture up to 57 percent of the remaining energy not captured by the tensor network alone. We conclude by discussing further ways to improve our approach.