Compact localized fermions and Ising anyons in a chiral spin liquid

Quasiparticle hybridization remains a major challenge in realizing and controlling exotic states of matter in existing quantum simulation platforms. We report the absence of hybridization for compact localized states (CLSs) emerging in the chiral spin liquid described by the Yao-Kivelson model. The CLS forms due to destructive quantum interference at fine-tuned coupling constants and populates perfectly flat quasiparticle bands on an effective kagome lattice. Using a formalism for general Majorana-hopping Hamiltonians, we derive exact expressions for CLSs 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>π</a:mi> </a:math> -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.