The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

TL;DR

This study investigates the quantum phase transition in the Hubbard model on a honeycomb lattice, revealing simultaneous semimetal to insulator and disordered to antiferromagnetic transitions with critical parameters consistent with the SU(2) Gross-Neveu universality class.

Contribution

The paper provides the first detailed numerical analysis of the critical coupling and exponents for the semimetal-antiferromagnetic Mott insulator transition on the honeycomb lattice using Hybrid Monte Carlo simulations.

Findings

Critical coupling $U_c=3.835(14)$ identified.

Critical exponents $ u=1.181(43)$ and $eta=0.898(37)$ calculated.

Transitions occur simultaneously and belong to the SU(2) Gross-Neveu universality class.

Abstract

The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $\nu=1.181(43)$ and $\beta=0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.