Spin-basis wavefunctions for the one-dimensional Kitaev model

Abstract

Magnetic phases with quantum entanglement are often expressed in terms of parton wavefunctions. Relatively few examples are known where wavefunctions can be directly written down in the spin basis. In this article, we consider the spin-$S$ Kitaev model in one dimension. For $S=1/2$, its eigenstates can be written using a Jordan-Wigner fermionic representation. Here, we present ground state wavefunctions for any $S$ directly in the spin basis. The states we propose are valence bond arrangements, with bonds having singlet or triplet character for $S=1/2$. For $S>1/2$, we use bond-states that serve as analogues of singlets and triplets. We establish the validity of our wavefunctions using a perturbative approach starting from an anisotropic limit, with key features surviving to all orders in perturbation theory. For half-integer $S$ and periodic boundaries, we have exponential ground state degeneracy. The ground states are subject to a nonlocal constraint. They have `triplets' superposed on a background of singlets, but with the total number of triplets constrained to be even. For integer $S$, a unique ground state emerges, composed purely of `triplets'. Our spin-basis wavefunctions, while not exact, capture the dominant weight of the ground state(s). We obtain good agreement against exact diagonalization wavefunctions and Jordan-Wigner spectra.