Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice

TL;DR

This paper explores the phase diagram of an SU(3) antiferromagnet on the kagome lattice, revealing trivial and topological spin liquids, including chiral spin liquids with potential edge modes, using analytical and numerical methods.

Contribution

It provides the first detailed phase diagram of an SU(3) kagome antiferromagnet, identifying novel trivial and topological spin liquid phases with chiral properties.

Findings

Identification of trivial AKLT-like and trimerized phases.

Discovery of a topological spin liquid with chiral edge modes.

Evidence for chiral spin liquids possibly exhibiting SU(3)$_1$ Wess-Zumino-Witten modes.

Abstract

Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical developments and various numerical techniques, namely exact Lanczos diagonalizations and tensor network variational approaches, we find a rich phase diagram with non-topological (``trivial") and topological (possibly chiral) gapped spin liquids (SLs). Trivial spin liquids include an Affleck-Kennedy-Lieb-Tasaki (AKLT)-like phase and a trimerized phase, the latter breaking the inversion center between the up and down triangles of the kagome lattice. A topological SL is stabilized in a restricted part of the phase diagram by the time-reversal symmetry breaking (complex) 3-site permutation term. Analyzing the chiral edge modes of this topological SL on long cylinders or on finite disks, we have come up with two competing scenarios, either a CSL or a double Chern-Simon SL characterized by a single or by two counter-propagating Wess-Zumino-Witten SU(3)$_1$ chiral mode(s), respectively. In the vicinity of the extended ferromagnetic region we have found a magnetic phase corresponding either to a modulated canted ferromagnet or to a uniform partially magnetized ferromagnet.