The $1/N$ Expansion and Spin Correlations in Constrained Wavefunctions

Details The $1/N$ Expansion and Spin Correlations in Constrained Wavefunctions The $1/N$ Expansion and Spin Correlations in Constrained Wavefunctions

1992-12-14

arxiv.org/abs/cond-mat/9212019v1

Physics

Condensed Matter

36 pages, LaTeX

Scientific paper

10.1103/PhysRevB.47.5118

We develop a large-N expansion for Gutzwiller projected spin states. We consider valence bonds singlets, constructed by Schwinger bosons or fermions, which are variational ground states for quantum antiferromagnets. This expansion is simpler than the familiar expansions of the quantum Heisenberg model, and thus more instructive. The diagrammatic rules of this expansion allow us to prove certain identities to all orders in 1/N. We derive the on-site spin fluctuations sum rule for arbitrary N. We calculate the correlations of the one dimensional Valence Bonds Solid states and the Gutzwiller Projected Fermi Gas upto order 1/N. For the bosons case, we are surprised to find that the mean field, the order 1/N and the exact correlations are simply proportional. For the fermions case, the 1/N correction enhances the zone edge singularity. The comparison of our leading order terms to known results for N=2, enhances our understanding of large-N approximations in general.

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