Hardcore dimer aspects of the SU(2) Singlet wavefunction

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.

5 pages, 2 figures

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Cited by in corpus (10)

• Quantum entanglement in condensed matter systems
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Master equation approach to computing RVB bond amplitudes
• The spherical sector of the Calogero model as a reduced matrix model
• Valence bond entanglement entropy of frustrated spin chains
• Shared Information in Stationary States at Criticality
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Entanglement entropy and localization in disordered quantum chains
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Entanglement of quantum spin systems: a valence-bond approach