Simulating both parity sectors of the Hubbard Model with Tensor Networks

TL;DR

This paper introduces a tensor network method using PEPS to accurately simulate the Hubbard model's ground states, including challenging cases where Monte Carlo methods fail, and presents a novel approach for simulating odd fermion sectors.

Contribution

It develops a PEPS-based imaginary time evolution method capable of simulating both parity sectors of the Hubbard model, including odd fermion number states, with improved stability and accuracy.

Findings

Accurate ground state estimations for Hubbard model with PEPS.

Linear scaling in lattice size for simulations.

Novel method for simulating odd fermion sectors.

Abstract

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical potential is one such problem. Our method is based on projected entangled pair states (PEPS) using imaginary time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably. In particular it shows near to optimal, that is linear, scaling in lattice size. We also present a novel approach to directly simulate the subspace with an odd number of fermions. It allows to independently determine the ground state in both sectors. Without a chemical potential this corresponds to half filling and the lowest energy state with one additional electron or hole. We identify several stability issues, such as degenerate ground states and large single particle gaps, and provide possible fixes.