Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state

TL;DR

This study uses advanced tensor network methods to determine that the plaquette valence-bond crystal is the true ground state of the SU(3) Heisenberg model on the honeycomb lattice, resolving previous conflicting predictions.

Contribution

The paper provides the first systematic iPEPS analysis confirming the plaquette state as the ground state, clarifying the nature of competing states in the SU(3) model.

Findings

Plaquette state is energetically favored at large bond dimension D.

Dimerized state has lower energy at small D.

Both states are non-chiral flux states.

Abstract

Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.