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We study the exotic quantum statistical behavior of composite particle ofdouble-spin cluster and quasiparticle of triple-spin cluster in a four-spinquantum model. We constructed a four spin-1/2 model on a triangular starlattice but added frustrated coupling terms of plaquette quasiparticles. Theeigenstates of this model are maximal entangled quantum states likeGreenberger-Horne-Zeilinger state and Yeo-Chua's genuine four-qubit entangledstate. We generalized the conventional definition for quantum statistics of twoelementary particles to composite particle of multispin clusters.Greenberger-Horne-Zeilinger state and Yeo-Chua's genuine four-qubit entangledstate showed different behavior according to this generalized definition. Thequantum statistical behavior of the composite particle of double-spin clusteris neither boson nor fermion in ground state and some intermediate excitedstates. The triple-spin cluster of this model is eigen-quasiparticles. Weperform permutation operation on the eigenstates of triple-spin plaquetteoperator according to this generalized definition for quantum statistics ofmulti-spin clusters, the statistical matrix of exchanging two triple-spinquasiparticles is far beyond fermion and boson. The von Neumann entropy of thetriple-spin quasiparticle is also highly nontrivial. These nontrivial quantumstatistical behavior of plaquette quasiparticles is helpful for decoding thenon-abelian anyons in Kitaev honeycomb model.

Exotic quantum statistics of composite particles and frustrated quasiparticles