Resonating-valence-bond structure of Gutzwiller-projected superconducting wave functions

TL;DR

This paper explores the resonating-valence-bond structure of Gutzwiller-projected superconducting wave functions, revealing how loop coverings and topological order relate in these complex quantum states.

Contribution

It extends the RVB framework to Gutzwiller-projected states with nodes, providing a new path integral representation and insights into topological order.

Findings

Loop statistical behavior is renormalized by projection.

Path integral over loop coverings describes RVB states.

Topological order relates to loop statistics.

Abstract

Gutzwiller-projected (GP) wave functions have been widely used for describing spin-liquid physics in frustrated magnets and in high-temperature superconductors. Such wave functions are known to represent states of the resonating-valence-bond (RVB) type. In the present work I discuss the RVB structure of a GP singlet superconducting state with nodes in the spectrum. The resulting state for the undoped spin system may be described in terms of the "path integral" over loop coverings of the lattice, thus extending the known construction for RVB states. The problem of the topological order in GP states may be reformulated in terms of the statistical behavior of loops. The simple example of the projected d-wave state on the square lattice demonstrates that the statistical behavior of loops is renormalized in a nontrivial manner by the projection.