Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice

TL;DR

This paper studies simple $SU(2)$-invariant wave functions on the square lattice that model spin liquids, revealing algebraic decay of correlations and modulation linked to topological invariants, with implications for related Hamiltonians.

Contribution

It demonstrates that certain valence-bond wave functions exhibit algebraic four-point correlations and spatial modulation, connecting topological invariants to physical properties.

Findings

Four-point correlations decay algebraically with exponent 1.16(4)

Correlators are spatially modulated by a wave-vector related to topological invariants

Implications for gapped spin and gapless non-magnetic excitations in related Hamiltonians

Abstract

We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave-functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent $1.16(4)$. This is reminiscent of the {\it classical} dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modulated according to a wave-vector related to the topological invariants. We conclude that a recently proposed spin Hamiltonian that stabilizes the here considered wave-function(s) as its (degenerate) ground-state(s) should exhibit gapped spin and gapless non-magnetic excitations.