Magnetism and charge order in the honeycomb lattice

TL;DR

This study uses quantum Monte Carlo simulations to explore how electron-phonon interactions influence phase transitions and ground state properties in the Hubbard-Holstein model on a honeycomb lattice, revealing detailed phase diagrams.

Contribution

It provides the first comprehensive phase diagram of the Hubbard-Holstein model on a honeycomb lattice, including effects of phonon frequency on phase transitions.

Findings

Identified semimetal-to-insulator quantum critical points.

Determined behavior of antiferromagnetic and charge-density wave phases.

Mapped ground state phase diagram for various phonon frequencies.

Abstract

Despite being relevant to better understand the properties of honeycomb-like systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on \textit{interacting} Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings represent a complete description of the model, and may shed light on the emergence of many-body properties in honeycomb-like systems.