The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice

TL;DR

This paper systematically analyzes the antiferromagnetic quantum phase transition in the hexagonal Hubbard Model using Monte Carlo methods, providing precise critical exponents and a comprehensive operator treatment.

Contribution

It offers a unified operator analysis and a controlled Monte Carlo study of the phase transition, improving the accuracy of critical exponent determination.

Findings

Critical exponent β=0.898(37) for the transition

Enhanced consistency in Monte Carlo critical exponent measurements

Comprehensive operator treatment applicable to strongly correlated systems

Abstract

We provide a unified, comprehensive treatment of all operators that contribute to the anti-ferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $\beta=0.898(37)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.