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

TL;DR

This study uses advanced Monte Carlo simulations to precisely identify the critical point and exponents of the Mott insulator transition in the honeycomb Hubbard model, providing insights into its universality class.

Contribution

We perform a high-precision analysis of the semimetal-Mott insulator transition in the honeycomb Hubbard model using improved Hybrid Monte Carlo methods, estimating critical parameters and discussing universality.

Findings

Critical coupling $U_c/=3.834(14)$ identified.

Critical exponent $z u=1.185(43)$ measured.

Preliminary order parameter exponent $eta=1.095(37)$ estimated.

Abstract

We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/\kappa=3.834(14)$ and the critical exponent $z\nu=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $\beta=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.