Two-orbital Schwinger Boson Representation of Spin-One: Application to a Non-abelian Spin Liquid with Quaternion Gauge Field

TL;DR

This paper introduces a two-orbital Schwinger boson framework for spin-1 systems, enabling the microscopic modeling of a non-abelian spin liquid with quaternion gauge fields, which was previously inaccessible with standard methods.

Contribution

It develops a novel two-orbital Schwinger boson representation for spin-1, facilitating the construction of a microscopic mean-field and wavefunction for a non-abelian quaternion spin liquid.

Findings

Constructed a mean-field state for the quaternion spin liquid.

Produced a superposition of AKLT loop configurations as a wavefunction.

Proposed generalizations to higher spin systems with complex gauge structures.

Abstract

A non-abelian spin liquid in triangular lattice spin-1 systems was recently formulated in the form of continuum field theory [T. Grover, and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011); Cenke Xu, A.W.W. Ludwig, arXiv:1012.5671]. It has spin-1/2 bosonic spinons coupled to emergent quaternion gauge fields, and can be obtained by quantum disordering a non-collinear spin nematic order hypothesized to describe NiGa_2S_4 [H. Tsunetsugu, and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006)], However a microscopic lattice description, e.g. the lattice spinon (mean-field) Hamiltonian and the spin wavefunction, has been missing, and it has been noted that the standard Schwinger boson or bosonic triplon representations of spin-1 cannot describe this spin liquid. In this paper a two-orbital Schwinger boson representation for spin-1 systems is developed and used to construct a mean-field description of this quaternion spin liquid. Projecting the mean-field state produces a prototype wavefunction, which is a superposition of close-packed AKLT loop configurations with nontrivial amplitudes. This new formalism and related wavefunctions may be generalized to higher spin systems and can possibly produce spin liquid states with even richer emergent gauge structures.