Non-Abelian Chiral Spin Liquid on the Kagome Lattice

TL;DR

This paper constructs and analyzes non-Abelian chiral spin liquids on the kagome lattice using Gutzwiller-projected superconductors, confirming their topological nature and proposing a Hamiltonian to stabilize them.

Contribution

It demonstrates the realization of non-Abelian chiral spin liquids on the kagome lattice via projected superconductors and confirms their topological properties through modular matrix calculations.

Findings

Confirmed non-Abelian topological order via modular matrices

Matched chiral central charge with field theory predictions

Observed phase transition to Abelian spin liquid

Abstract

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.