Dimer description of the SU(4) antiferromagnet on the triangular lattice

Abstract

In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin" models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg" model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.

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Cited by in corpus (7)

• The Orbitally Selective Mott Phase in Electron Doped Twisted TMDs: A Possible Realization of the Kondo Lattice Model
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Moments and multiplets in moiré materials: A pseudo-fermion functional renormalization group for spin-valley models
• Spin-valley magnetism on the triangular moiré lattice with SU(4) breaking interactions