Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice

TL;DR

This paper classifies symmetric $Z_2$ spin liquids on the triangular lattice, identifies promising candidate phases, and explores their neighboring magnetic and valence bond solid orders, providing insights into the phase diagram of spin-$1/2$ systems.

Contribution

It systematically classifies $Z_2$ spin liquids on the triangular lattice and identifies promising candidate phases with potential experimental relevance.

Findings

20 distinct $Z_2$ spin liquid phases identified

2 candidate phases can realize gapped $Z_2$ spin liquids with extended amplitudes

One phase connected to 120-degree Neel order via continuous transition

Abstract

Motivated by recent numerical discovery of a gapped spin liquid phase in spin-$1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model, we classify symmetric $Z_2$ spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, 8 of which have their counterparts in the Schwinger-boson representation. Among them we identify 2 promising candidates (#1 and #20), which can realize a gapped $Z_2$ spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond solid patterns, and find one state (#20) that is connected to 120-degree Neel order by a continuous quantum phase transition. We also identify gapped nematic $Z_2$ spin liquids in the neighborhood of the symmetric states and find 3 promising candidates (#1, #6 and #20).