Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice

TL;DR

This paper demonstrates that the SU(4) Heisenberg model on a square lattice exhibits spontaneous dimerization and additional symmetry breaking, resulting in a gapless spectrum despite broken translational symmetry, contrasting with lower SU(N) cases.

Contribution

It reveals the unique dimerization and symmetry-breaking phenomena in the SU(4) model on the square lattice, using multiple computational and theoretical methods.

Findings

SU(4) model undergoes spontaneous dimerization

Additional SU(4) symmetry breaking occurs

Results in a gapless spectrum despite translational symmetry breaking

Abstract

Using infinite projected entangled pair states (iPEPS), exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast to its SU(2) and SU(3) counterparts, which develop Neel and three-sublattice stripe-like long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irrep, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.