Exotic quantum statistics of composite particles and frustrated quasiparticles

TL;DR

This paper explores the exotic quantum statistics of composite and quasiparticles in a frustrated four-spin model, revealing non-abelian anyon-like behavior and entanglement properties that extend traditional quantum statistics.

Contribution

It generalizes quantum statistics to multispin clusters and demonstrates their nontrivial behavior in a frustrated lattice model.

Findings

Composite double-spin particles are neither bosons nor fermions in certain states.

Triple-spin quasiparticles exhibit statistics far beyond fermions and bosons.

The entropy of triple-spin quasiparticles is highly nontrivial.

Abstract

We study the exotic quantum statistical behavior of composite particle of double-spin cluster and quasiparticle of triple-spin cluster in a four-spin quantum model. We constructed a four spin-1/2 model on a triangular star lattice but added frustrated coupling terms of plaquette quasiparticles. The eigenstates of this model are maximal entangled quantum states like Greenberger-Horne-Zeilinger state and Yeo-Chua's genuine four-qubit entangled state. We generalized the conventional definition for quantum statistics of two elementary particles to composite particle of multispin clusters. Greenberger-Horne-Zeilinger state and Yeo-Chua's genuine four-qubit entangled state showed different behavior according to this generalized definition. The quantum statistical behavior of the composite particle of double-spin cluster is neither boson nor fermion in ground state and some intermediate excited states. The triple-spin cluster of this model is eigen-quasiparticles. We perform permutation operation on the eigenstates of triple-spin plaquette operator according to this generalized definition for quantum statistics of multi-spin clusters, the statistical matrix of exchanging two triple-spin quasiparticles is far beyond fermion and boson. The von Neumann entropy of the triple-spin quasiparticle is also highly nontrivial. These nontrivial quantum statistical behavior of plaquette quasiparticles is helpful for decoding the non-abelian anyons in Kitaev honeycomb model.