Journal
NUCLEAR PHYSICS B
Volume 750, Issue 3, Pages 142-178Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.nuclphysb.2006.05.032
Keywords
valence bonds; quantum spin systems; Heisenberg model
Categories
Ask authors/readers for more resources
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 conrelation 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. (c) 2006 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available