Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

TL;DR

This paper uses advanced numerical methods to study the SU(3) Heisenberg model on square and triangular lattices, confirming three-sublattice order with finite moments, and providing new insights into quantum fluctuations and ordering.

Contribution

The study provides the first numerical confirmation of three-sublattice order in the SU(3) Heisenberg model on both lattices, especially clarifying the ordered moment on the square lattice.

Findings

Triangular lattice exhibits three-sublattice order with finite moment.

Square lattice also shows three-sublattice order, with an ordered moment of 0.2-0.4.

Numerical results support predictions from flavor wave theory and previous studies.

Abstract

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [PRL 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0.2-0.4 in the thermodynamic limit.