Resonating valence bond wave functions and classical interacting dimer models

Damle, Kedar ; Dhar, Deepak ; Ramola, Kabir (2012) Resonating valence bond wave functions and classical interacting dimer models Physical Review Letters, 108 (24). Article ID 247216. ISSN 0031-9007

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Official URL: https://journals.aps.org/prl/abstract/10.1103/Phys...

Related URL: http://dx.doi.org/10.1103/PhysRevLett.108.247216

Abstract

We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for SU(g) spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of n-body potentials Vn, which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the n-body interaction Vn (n>1) is of order O(g−(n−1) ) for small g−1. The leading term is a two-body nearest-neighbor interaction V2(g) favoring two parallel dimers on elementary plaquettes. For SU(2) spins, using our calculated value of V2(g=2), we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as 1/|⃗r|α with α≈1.22. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give α≈1.20.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:112290
Deposited On:31 Jan 2018 04:29
Last Modified:31 Jan 2018 04:29

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