Stochastic and Tensor Network simulations of the Hubbard Model

TL;DR

This paper compares stochastic Hybrid Monte Carlo and Tensor Network methods for simulating the Hubbard model, highlighting their capabilities and limitations in studying quantum phase transitions in materials like graphene.

Contribution

It introduces and evaluates two numerical techniques—Hybrid Monte Carlo and Tensor Networks—for large-scale Hubbard model simulations, emphasizing their complementary strengths.

Findings

Hybrid Monte Carlo enables simulation of larger lattices.

Tensor Networks avoid the sign problem.

Methods have distinct advantages and limitations.

Abstract

The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it is used to describe graphene predicting a quantum phase transition from a semimetal to a Mott insulating state. In this work two different numerical techniques are presented that have been employed for simulations of the Hubbard model: The Hybrid Monte Carlo algorithm on the one hand allowed us to simulate unprecedentedly large lattices, whereas Tensor Networks can be used to completely avoid the sign problem. Respective strengths and weaknesses of the methods are discussed.