2006/05/03 by K. S. D. Beach, Anders W. Sandvik, A. W. Sandvik · 1 citation
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Magnetism in coordination complexes #Physics of Superconductivity and Magnetism #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1016/j.nuclphysb.2006.05.032
published as Nucl. Phys. B 750, 142 (2006) · 22 pages, 14 figures
arxiv created 2006/05/03 · openalex publication_date 2006/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a system with an even number of SU(2) spins, there is an overcomplete set of states--consisting of all possible pairings of the spins into valence bonds--that spans the S=0 Hilbert subspace. Operator expectation values in this basis are related to the properties of the closed loops that are formed by the overlap of valence bond states. We construct a generating function for spin correlation functions of arbitrary order and show that all nonvanishing contributions arise from configurations that are topologically irreducible. We derive explicit formulas for the correlation functions at second, fourth, and sixth order. We then extend the valence bond basis to include triplet bonds and discuss how to compute properties that are related to operators acting outside the singlet sector. These results are relevant to analytical calculations and to numerical valence bond simulations using quantum Monte Carlo, variational wavefunctions, or exact diagonalization.