Hardcore dimer aspects of the SU(2) Singlet wavefunction

TL;DR

This paper shows that all SU(2) singlet wavefunctions can be described using valence bond occupation numbers, linking quantum dimer features to spin correlations and entanglement measures, with implications for quantum magnetism and information.

Contribution

It introduces a rigorous characterization of SU(2) singlet states via valence bond occupation numbers, bridging quantum dimer concepts with spin correlation and entanglement measures.

Findings

SU(2) singlets can be characterized by valence bond occupation numbers.

Provides a rigorous basis for quantities measuring spin correlations and entanglement.

Demonstrates a functional mapping between spin Hilbert space and algebraic functions.

Abstract

We demonstrate that any SU(2) singlet wavefunction can be characterized by a set of Valence Bond occupation numbers, testing dimer presence/vacancy on pairs of sites. This genuine quantum property of singlet states (i) shows that SU(2) singlets share some of the intuitive features of hardcore quantum dimers, (ii) gives rigorous basis for interesting albeit apparently ill-defined quantities introduced recently in the context of Quantum Magnetism or Quantum Information to measure respectively spin correlations and bipartite entanglement and, (iii) suggests a scheme to define consistently a wide family of quantities analogous to high order spin correlation. This result is demonstrated in the framework of a general functional mapping between the Hilbert space generated by an arbitrary number of spins and a set of algebraic functions found to be an efficient analytical tool for the description of quantum spins or qubits systems.