Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions

TL;DR

This paper investigates the quantum phases of SU(N) Dirac fermions on a honeycomb lattice, revealing a transition from semimetal to valence bond crystal states with varying N, using quantum Monte Carlo simulations and large-N analysis.

Contribution

It provides the first detailed numerical and analytical study of SU(N) fermionic systems on the honeycomb lattice, identifying novel valence bond crystal phases and phase transitions.

Findings

Insulating state is a columnar valence bond crystal for large N.

Direct transition from semimetal to insulator at weak coupling.

Resonating valence bond plaquettes stabilize the SU(4) insulator.

Abstract

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half-filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.