Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators

TL;DR

This paper explores the phase diagram of two-dimensional SU(N) antiferromagnets on a triangular lattice, revealing a transition from ordered states to topological chiral spin liquids as the number of flavors increases, with implications for materials and cold atom systems.

Contribution

It identifies and characterizes topological chiral spin liquids and competing states in SU(N) Mott insulators on a triangular lattice, highlighting the role of flavor number in stabilizing these phases.

Findings

Cluster and ordered ground states dominate for N<6.

Increasing N promotes quantum fluctuations, leading to chiral spin liquids.

The chiral spin liquid state has an equivalent in square lattice SU(N) magnets.

Abstract

SU($N$) Mott insulators have been proposed and/or realized in solid-state materials and with ultracold atoms on optical lattices. We study the two-dimensional SU($N$) antiferromagnets on the triangular lattice. Starting from an SU($N$) Heisenberg model with the fundamental representation on each site in the large-$N$ limit, we perform a self-consistent calculation and find a variety of ground states including the valence cluster states, stripe ordered states with a doubled unit-cell and topological chiral spin liquids. The system favors a cluster or ordered ground state when the number of flavors $N$ is less than 6. It is shown that, increasing the number of flavors enhances quantum fluctuations and eventually transfer the clusterized ground states into a topological chiral spin liquids. This chiral spin liquid ground state has an equivalent for the square lattice SU($N$) magnets. We further identify the corresponding lowest competing states that represent another distinct type of chiral spin liquid states. We conclude with a discussion about the relevant systems and the experimental probes.