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Resonant Valance Bond Ground States on Corner-sharing Lattices

by Zhao Zhang, Cecilie Glittum

Submission summary

Authors (as registered SciPost users):

Cecilie Glittum

Abstract

The Hubbard model in the $U\to\infty$ limit has recently been shown to have resonant valence bond (RVB) ground states on the corner-sharing sawtooth and pyrochlore lattices in the dilute doping limit of a single vacancy. The two results were obtained by different approaches which do not apply to one another. We make the first step towards unifying them by studying the quasi-1D lattice of a pyrochlore stripe, where all corners are not shared between two tetrahedra, and the valence bond configurations are not fixed by the location of the vacancy. The energy level ordering of irreducible representations of each tetrahedron shows that a chain of them has exponentially degenerate partial RVB or dimer-monomer ground states where each tetrahedron hosts one spin-$1/2$ monomer and one spin-$0$ dimer. The exact ground states in the infinitely long chain limit are analytically solved by introducing basis transformations between local Hilbert spaces of neighboring tetrahedra, and its energy agrees with the extrapolation of numerical exact diagonalization results of finite sized systems.

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