Compact localized fermions and Ising anyons in a chiral spin liquid

TL;DR

This paper demonstrates the existence of compact localized fermions and Majorana zero modes in a chiral spin liquid, revealing non-hybridized flat bands and enabling non-Abelian anyon braiding, advancing quantum simulation of topological matter.

Contribution

It provides exact expressions for compact localized states in the Yao-Kivelson model and constructs Majorana zero modes for non-Abelian braiding, highlighting new pathways for topological quantum computation.

Findings

Compact localized states occur without hybridization.

Exact formulas for CLS in different flux configurations.

Construction of Majorana zero modes for Ising anyons.

Abstract

Quasiparticle hybridization remains a major challenge to realizing and controlling exotic states of matter in existing quantum simulation platforms. We report the absence of hybridization for compact localized states (CLS) emerging in the chiral spin liquid described by the Yao-Kivelson model. The CLS form due to destructive quantum interference at fine-tuned coupling constants and populate perfectly flat quasiparticle bands on an effective kagome lattice. Using a formalism for general Majorana-hopping Hamiltonians, we derive exact expressions for CLS for various flux configurations and both for the topological and trivial phases of the model. In addition to finite-energy matter fermions with characteristic spin-spin correlations, we construct compact localized Majorana zero modes attached to $\pi$-flux excitations, which enable non-Abelian braiding of Ising anyons with minimal separation. Our results inform the quantum simulation of topologically ordered states of matter and open avenues for exploring flat-band physics in quantum spin liquids.