Sign structures for short-range RVB states on small kagome clusters

TL;DR

This paper extends the Schwinger boson approach to construct and analyze resonating valence bond (RVB) wave functions on small kagome clusters, revealing their energy band structure and sign configurations.

Contribution

It introduces a method to determine RVB sign structures for low-energy states on small kagome clusters, linking classical states to quantum RVB states.

Findings

RVB states form a narrow energy band on the 36-site cluster.

Superpositions of a few states reproduce low-energy spectra on the 12-site cluster.

Specific two-vison insertions accurately reproduce the ED ground state.

Abstract

We extended the Schwinger boson construction to obtain wave functions that are resonating valence bond (RVB) counterparts of the degenerate coplanar classical states on the Kagome lattice. We examined all 84 of them on the 36-site cluster and found that they form a narrow energy band. On the 12-site cluster, there are only four such states and their superpositions accurately account for the second through fourth exact diagonalization (ED) states, while the ED ground state is accurately reproduced by allowing a particular two-vison insertion on top of the q=0 RVB state. Thus, we have established the RVB sign structures for the low energy states on this cluster.