Topological and Trivial Valence-Bond Orders in Higher-Spin Kitaev Models

TL;DR

This paper explores the quantum phases of higher-spin Kitaev models, revealing distinct valence-bond orders and symmetry-breaking phenomena using advanced tensor network methods.

Contribution

It provides the first detailed tensor network analysis of higher-spin Kitaev models, identifying different bond-ordered phases and their topological or non-topological nature.

Findings

Spin-1, 3/2, and 2 models exhibit distinct bond-ordered phases.

All phases show translational symmetry breaking with tripled unit cells.

Different orders are understood through theoretical analysis and tensor network validation.

Abstract

We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and non-topological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.