Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition

TL;DR

This paper explores the phase diagram of SU(N) Dirac fermions with plaquette interactions on a square lattice, revealing diverse quantum phases and phase transitions, including Gross-Neveu criticality and first-order transitions, through large-scale quantum Monte Carlo simulations.

Contribution

It extends previous studies to SU(6) and SU(8), uncovering a rich variety of quantum phases and phase transitions driven by extended plaquette interactions in Dirac fermion systems.

Findings

Identification of multiple quantum phases such as Dirac semimetal, VBS, and spin liquid.

Observation of Gross-Neveu chiral transitions with emergent symmetry.

Detection of first-order transition between different VBS states.

Abstract

Inspired by our recent works[1, 2] of SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase digram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases such as the Dirac semimetal, the antiferromagnetic Mott insulator, valence bond solid (VBS) and the Dirac spin liquid and phase transitions including the Gross-Neveu chiral transitions with emergent continuous symmetry, the deconfined quantum criticality and the first order transition between interaction-driven columnar VBS and plaquette VBS. These rich phenomena coming from the simple-looking lattice models, firmly convey the message that the interplay between the $SU(N)$ Dirac fermions -- with enhanced internal symmetries -- and extended plaquette interactions -- beyond the on-site Hubbard type -- is the new playground to synthesise novel highly entangled quantum matter both at the model level and with experimental feasibilities.