Attractive Hubbard Model on a Honeycomb Lattice

TL;DR

This study investigates the phase transitions and superfluid behavior of the attractive Hubbard model on a honeycomb lattice using quantum Monte Carlo simulations, revealing a quantum phase transition and BCS-molecular crossover.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the attractive Hubbard model on a honeycomb lattice, identifying a quantum phase transition and superfluid crossover regimes.

Findings

Quantum phase transition at U_c/t between 5.0 and 5.1 from semi-metal to superfluid with density order.

Superfluid crossover from BCS to molecular regime with doping and increasing interaction.

Spectral function analysis reveals pairing and phase coherence development.

Abstract

We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the system undergoes a quantum phase transition at 5.0 < U_c/t < 5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered.