Some formal results for the valence bond basis

Details Some formal results for the valence bond basis Some formal results for the valence bond basis

2006-05-03

arxiv.org/abs/cond-mat/0605103v1

Nucl. Phys. B 750, 142 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

22 pages, 14 figures

Scientific paper

10.1016/j.nuclphysb.2006.05.032

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.

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