Competing order in the fermionic Hubbard model on the hexagonal graphene lattice

TL;DR

This paper investigates the phase diagram of the fermionic Hubbard model on a hexagonal lattice, exploring the competition between spin-density and charge-density waves using Hybrid-Monte-Carlo simulations without explicit symmetry breaking.

Contribution

It introduces a simulation approach that avoids explicit sublattice symmetry breaking and compares results with Hartree-Fock predictions for the Hubbard model on a hexagonal lattice.

Findings

Critical coupling for spin-density wave identified

Phase diagram qualitatively matches Hartree-Fock results

Method avoids fermion sign problem and symmetry breaking artifacts

Abstract

We study the phase diagram of the fermionic Hubbard model on the hexagonal lattice in the space of on-site and nearest neighbor couplings with Hybrid-Monte-Carlo simulations. With pure on-site repulsion this allows to determine the critical coupling strength for spin-density wave formation with the standard approach of introducing a small mass term, explicitly breaking the sublattice symmetry. The analogous mass term for charge-density wave formation above a critical nearest-neighbor repulsion, on the other hand, would introduce a fermion sign problem. The competition between the two and the phase diagram in the space of the two coouplings can however be studied in simulations without explicit sublattice symmetry breaking. Our results compare qualitatively well with the Hartree-Fock phase diagram. We furthermore demonstrate how spin-symmetry breaking by the Euclidean time discretization can be avoided also, when using an improved fermion action based on an exponetial transfer matrix with exact sublattice symmetry.