Variational Monte Carlo simulations using tensor-product projected states

TL;DR

This paper introduces a variational Monte Carlo method combining tensor-network techniques with trial wave functions to efficiently approximate ground states of quantum many-body systems, including those with complex entanglement.

Contribution

It presents a novel tensor-product projected state approach that reduces bond dimensions and encodes fermion signs, improving ground state approximations.

Findings

Accurately approximates ground-state energies for 2D bosonic systems

Effectively encodes fermion sign structures in wave functions

Reduces computational complexity compared to traditional tensor networks

Abstract

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.