Zigzag antiferromagnets in the SU(3) Hubbard model on the square lattice

TL;DR

This paper investigates the phase diagram of the SU(3) Hubbard model at 1/3-filling on a square lattice, revealing zigzag antiferromagnetic states and phase transitions using advanced tensor network methods.

Contribution

It provides the first detailed tensor network study of the SU(3) Hubbard model, identifying zigzag antiferromagnetic phases and analyzing their stability and energy contributions.

Findings

Reproduces known 3-sublattice antiferromagnetic order in strong coupling limit.

Discovers zigzag antiferromagnetic states at intermediate interactions.

Identifies phase transitions with discontinuous changes in order parameters.

Abstract

SU(N) Hubbard models exhibit a rich variety of phases, which may be realized through quantum simulation with ultracold atomic gases in optical lattices. In this work we study the Mott insulating phases of the SU(3) Hubbard model at 1/3-filling using infinite projected entangled-pair states, optimized with both imaginary time evolution and variational optimization. In the limit of strong interactions we reproduce the antiferromagnetic 3-sublattice ordered state previously identified in the SU(3) Heisenberg model. At intermediate interaction strength we find antiferromagnetic states exhibiting zigzag patterns of different lengths, in agreement with previous Hartree-Fock and constrained-path auxiliary-field quantum Monte Carlo calculations. We study the color order parameter and energy anisotropy, which are discontinuous across the phase transitions. Finally, we analyze the different energy contributions in two competing phases, identifying low-energy bonds at the corners of the zigzag that help stabilize the zigzag states.