# Quantum spin liquid in the semiclassical regime

## TL;DR

This paper demonstrates the existence of a $Z_2$ quantum spin liquid ground state in a semiclassical large-$S$ magnet modeled by the spin-$S$ Kitaev honeycomb model, revealing topological order and distinct energy gaps.

## Contribution

It shows that quantum spin liquids can occur in the semiclassical, large-$S$ limit, extending the understanding of topological order beyond low-spin quantum regimes.

## Key findings

- Existence of $Z_2$ quantum spin liquid in large-$S$ limit
- Presence of topological and symmetry-related degeneracies
- Two distinct energy gaps with different scaling behaviors

## Abstract

Quantum spin liquids have been at the forefront of correlated electron research ever since their original proposal in 1973, and the realization that they belong to the broader class of intrinsic topological orders, along with the fractional quantum Hall states. According to received wisdom, quantum spin liquids can arise in frustrated magnets with low spin $S$, where strong quantum fluctuations act to destabilize conventional, magnetically ordered states. Here we present a magnet that has a $Z_2$ quantum spin liquid ground state already in the semiclassical, large-$S$ limit. The state has both topological and symmetry related ground state degeneracy, and two types of gaps, a `magnetic flux' gap that scales linearly with $S$ and an `electric charge' gap that drops exponentially in $S$. The magnet is described by the spin-$S$ version of the spin-1/2 Kitaev honeycomb model, which has been the subject of intense studies in correlated electron systems with strong spin-orbit coupling, and in optical lattice realizations with ultracold atoms. The results apply to both integer and half-integer spins.