Resonant Valance Bond Ground States on Corner-sharing Lattices

• URL: http://arxiv.org/abs/2507.10471v2
• Date: Thu, 06 Nov 2025 15:40:50 GMT
• Title: Resonant Valance Bond Ground States on Corner-sharing Lattices
• Authors: Zhao Zhang, Cecilie Glittum,
• Abstract summary: We study the quasi-1D lattice of a pyrochlore stripe, where all corners are not shared between two tetrahedra.<n>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.<n>The exact ground states in the infinitely long chain limit are analytically solved by introducing basis transformations between local Hilbert spaces of neighboring tetrahedra.
• Score: 4.964333564104488
• License: http://creativecommons.org/licenses/by/4.0/
• 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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