The Hubbard model with fermionic tensor networks

TL;DR

This paper introduces a fermionic tensor network approach to simulate the Hubbard model on a honeycomb lattice, overcoming the sign problem and enabling the study of states at different fillings.

Contribution

It develops a fermionic projected entangled pair state method that allows simulation of the Hubbard model at half filling and with an extra electron, bypassing the sign problem.

Findings

Successfully computed energies at different fillings

Accessed states previously unreachable by Monte Carlo methods

Demonstrated the effectiveness of fermionic tensor networks for strongly correlated systems

Abstract

Many electromagnetic properties of graphene can be described by the Hubbard model on a honeycomb lattice. However, this system suffers strongly from the sign problem if a chemical potential is included. Tensor network methods are not affected by this problem. We use the imaginary time evolution of a fermionic projected entangled pair state, which allows to simulate both parity sectors independently. Incorporating the fermionic nature on the level of the tensor network allows to fix the particle number to be either even or odd. This way we can access the states at half filling and with one additional electron. We calculate the energy and other observables of both states, which was not possible before with Monte Carlo methods.