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

Inspired by our recent works on 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 diagram 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 Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS anda plaquette VBS. These rich phenomena coming from 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 synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.

Automated summary

This study extends the large-scale quantum Monte Carlo investigations of Dirac fermions with SU(6) and SU(8) symmetries subjected to plaquette interactions on a square lattice. The rich phase diagram exhibits various emerging quantum phases and phase transitions.