# Spin chain network construction of chiral spin liquids

## TL;DR

This paper introduces a honeycomb lattice model of spin-1/2 chains with three-spin interactions that realizes a chiral spin liquid phase, exhibiting quantized spin Hall conductance and semionic spinon excitations, with potential for broader applications.

## Contribution

It provides a controlled analytical construction of chiral spin liquids using spin chain networks, connecting lattice models to boundary conformal field theory and topological phases.

## Key findings

- Realization of a Kalmeyer-Laughlin chiral spin liquid phase.
- Quantized spin Hall conductance demonstrated.
- Elementary excitations are localized spinons with semionic statistics.

## Abstract

We show that a honeycomb lattice of Heisenberg spin-$1/2$ chains with three-spin junction interactions allows for controlled analytical studies of chiral spin liquids (CSLs). Tuning these interactions to a chiral fixed point, we find a Kalmeyer-Laughlin CSL phase which here is connected to the critical point of a boundary conformal field theory. Our construction directly yields a quantized spin Hall conductance and localized spinons with semionic statistics as elementary excitations. We also outline the phase diagram away from the chiral point where spinons may condense. Generalizations of our approach can provide microscopic realizations for many other CSLs.