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.
Highlights
We considered SU(4) spins in the six-dimensional representation, on the triangular lattice, with nearest-neighbor antiferromagnetic interactions
The study of the the associated dimer model led us to conjecture that the ground state of the SU(4) model may be a 12-site valence bond solid (VBS)
As a first step in this direction, we carried out preliminary calculations in addition to those reported in this paper, using the infinite density matrix renormalization group (DMRG) method on width-four cylinders
Summary
Frustrated quantum antiferromagnets may possess non-magnetic ground states, avoiding spin order through short or long range entanglement of spins. Like the familiar S=1/2 SU(2) spins, pairs of spins in this representation may form a singlet “valence bond”, so that there is a natural “dimer” picture upon which non-magnetic states may be based It has been shown by Rokhsar [4] that at N = ∞, dimerized states (i.e. products of singlet bonds) are the ground states in the self-conjugate representation for a very wide class of lattices and exchange interactions (including almost all those of physical interest). The simplest quantum dimer model on the triangular lattice was argued to possess a 2 spin liquid ground state [22] With these motivations, we study the aforementioned SU(4) model on the triangular lattice both analytically and numerically.
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