Quantum phase transitions in the honeycomb-lattice Hubbard model

TL;DR

This study investigates quantum phase transitions in the honeycomb-lattice Hubbard model using the variational cluster approximation, revealing a second-order antiferromagnetic transition and a wide paramagnetic insulating phase.

Contribution

It provides new insights into the critical interaction values and the nature of the phase transitions, including the semimetal-insulator transition at infinitesimal interaction.

Findings

Critical interaction for antiferromagnetic transition matches quantum Monte Carlo results.

The semimetal-insulator transition occurs at infinitesimally small interaction.

The paramagnetic insulating phase exhibits complex electron behavior beyond a simple Heisenberg model.

Abstract

Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide interaction range. A crossover behavior of electrons from itinerant to localized character found in the calculated single-particle excitation spectra and short-range spin correlation functions indicates that an effective spin model for the paramagnetic insulating phase is far from a simple Heisenberg model with a nearest-neighbor exchange interaction.