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

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.

24 pages, 25 figures, 4 tables

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• Exploiting the Hermitian symmetry in tensor network algorithms
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Chiral Edge States Emerging on Anyon-Net
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Variational optimization of projected entangled-pair states on the triangular lattice
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS
• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice