A density of states approach to the hexagonal Hubbard model at finite density

TL;DR

This paper applies the LLR method to the honeycomb Hubbard model to compute the density of states and analyze the sign problem, demonstrating advantages at stronger interactions and proposing future improvements.

Contribution

It introduces the use of the LLR method for the honeycomb Hubbard model and develops reconstruction schemes to extract physical observables from the density of states.

Findings

LLR method effectively computes the density of states for the model.

Advantage over reweighting increases with interaction strength.

Potential for future improvements in handling the sign problem.

Abstract

We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice. We compute the generalized density of states of the average Hubbard field and divise two reconstruction schemes to extract physical observables from this result. By computing the particle density as a function of chemical potential we assess the utility of LLR in dealing with the sign problem of this model, which arises away from half filling. We show that the relative advantage over brute-force reweighting grows as the interaction strength is increased and discuss possible future improvements.