Chiral d-wave RVB state on honeycomb lattice as a generalized staggered flux phase

TL;DR

This paper introduces a chiral d-wave RVB state on the honeycomb lattice, generalizing the staggered flux phase, and demonstrates its properties, symmetry, and relevance as a variational state for the Heisenberg model.

Contribution

It proposes a new chiral d-wave RVB state on the honeycomb lattice, analyzing its symmetry, gauge structure, and variational effectiveness compared to previous models.

Findings

The state is a fully symmetric spin liquid with positive wave function.

The critical pairing strength for the $ ext{pi}$-flux phase is $rac{ ext{sqrt}(2)}$.

The state enhances spin correlations beyond mean field predictions.

Abstract

We show the chiral d-wave RVB state on honeycomb lattice stands as a natural generalization of the staggered flux phase on square lattice. Although the state is generated from a time reversal symmetry broken mean field ansatz, it actually represents a fully symmetric spin liquid state with a positive definite wave function in the sense of Marshall sign rule for unfrustrated antiferromagnets. The evolution of the state with the parameter $\Delta/\chi$ follows exactly the same manner as that of the staggered flux phase on square lattice. The critical pairing strength corresponding to the $\pi$-flux phase is found to be $\Delta/\chi=\sqrt{2}$. As a result of the geometric frustration between neighboring plaquette on honeycomb lattice, a direct generalization of the U(1) staggered flux pattern on square lattice to honeycomb lattice is impossible. Replacing it is the chiral d-wave state with $Z_{2}$ gauge structure. However, this $Z_{2}$ gauge structure is found to be ineffective after Gutzwiller projection and the system does not support topological degeneracy. The chiral d-wave RVB state is also found to be a rather good variational state for the Heisenberg model on honeycomb lattice. The spin correlation of the chiral d-wave state is found to be greatly enhanced as compared to the mean field prediction.