Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory

TL;DR

This paper classifies possible spin liquid states on a honeycomb lattice using Projective Symmetry Group and Schwinger fermion mean-field theory, identifying a fully gapped candidate state near the Mott transition and exploring its realization in Hubbard models.

Contribution

It systematically classifies spin liquid states on a honeycomb lattice and proposes the Sublattice Pairing State as the candidate phase near the Mott transition.

Findings

Identified the Sublattice Pairing State as a fully gapped spin liquid candidate.

Proposed a continuous phase transition scenario from SPS to semimetal.

Provided guidelines for future variational studies of Gutzwiller wavefunctions.

Abstract

Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using Projective Symmetry Group, we classify all the possible spin liquid states by Schwinger fermion mean-field approach. We find there is only one fully gapped spin liquid candidate state: "Sublattice Pairing State" that can be realized up to the 3rd neighbor mean-field amplitudes, and is in the neighborhood of the Mott transition. We propose this state as the spin liquid phase discovered in the numerical work. To understand whether SPS can be realized in the Hubbard model, we study the mean-field phase diagram in the $J_1-J_2$ spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.