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

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.

11 pages, 12 figures, small changes, added more references

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• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• SU(6) Heisenberg model on the honeycomb lattice: competition between plaquette and chiral order
• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• SU(3) Fermions on the Honeycomb Lattice at 1/3-Filling
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Highly frustrated magnetism in relativistic ${\mathbf{d}}^4$ Mott insulators: Bosonic analog of Kitaev honeycomb model
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Generating function for projected entangled-pair states
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice
• Spin liquid phases of alkaline-earth-metal atoms at finite temperature
• SU(3) trimer resonating-valence-bond state on the square lattice
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Stabilization of the chiral phase of the SU($6m$) Heisenberg model on the honeycomb lattice with $m$ particles per site for $m$ larger than 1
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model