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Exotic quantum statistics of composite particles and frustrated quasiparticles

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.