Combination of Tensor Network States and Green's function Monte Carlo

TL;DR

This paper introduces a hybrid approach combining Tensor Network States and Green's function Monte Carlo to efficiently study quantum many-body ground states, reducing computational costs and systematic errors.

Contribution

It presents a novel method integrating PEPS and GFMC, leveraging their strengths to improve accuracy and efficiency in quantum ground state calculations.

Findings

Reduced computational complexity in GFMC contractions

Variational energy guarantees from GFMC results

Benchmark validation on J1-J2 Heisenberg model

Abstract

We propose an approach to study the ground state of quantum many-body systems in which Tensor Network States (TNS), specifically Projected Entangled Pair States (PEPS), and Green's function Monte Carlo (GFMC) are combined. PEPS, by design, encode the area law which governs the scaling of entanglement entropy in quantum systems with short range interactions but are hindered by the high computational complexity scaling with bond dimension (D). GFMC is a highly efficient method, but it usually suffers from the infamous negative sign problem which can be avoided by the fixed node approximation in which a guiding wave function is utilized to modify the sampling process. The trade-off for the absence of negative sign problem is the introduction of systematic error by guiding wave function. In this work, we combine these two methods, PEPS and GFMC, to take advantage of both of them. PEPS are very accurate variational wave functions, while at the same time, only contractions of single-layer tensor network are necessary in GFMC, which reduces the cost substantially. Moreover, energy obtained in GFMC is guaranteed to be variational and lower than the variational energy of the guiding PEPS wave function. Benchmark results of $J_1$-$J_2$ Heisenberg model on square lattice are provided.