Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions

TL;DR

This study explores three-dimensional bipartite lattices with valence-bond wave functions, revealing coexistence of magnetic order and dipolar correlations, and demonstrates how simple modifications can lead to different ordering phenomena.

Contribution

It provides large-scale Monte Carlo evidence of coexistence of magnetic order and dipolar correlations in 3D valence-bond wave functions, highlighting their generic nature and tunability.

Findings

Long-range magnetic order coexists with dipolar four-spin correlations.

Similar properties are observed on the diamond lattice.

Simple modifications can induce different ordering behaviors.

Abstract

We investigate nearest-neighbor valence-bond wave functions on bipartite three-dimensional lattices. By performing large-scale Monte Carlo simulations, we find that long-range magnetic order coexists with dipolar four-spin correlations on the cubic lattice, this latter feature being reminiscent of the Coulomb phase for classical dimers on the same lattice. Similar properties are found for the lower-coordination diamond lattice. While this suggests that the coexistence of magnetic order and dipolar four-spin correlations is generic for bipartite three-dimensional lattices, we show that simple generalizations of these wave functions can encode different ordering behaviors.