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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.23639 |
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| _version_ | 1866912794319781888 |
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| author | Bhola, Ritesh Damle, Kedar |
| author_facet | Bhola, Ritesh Damle, Kedar |
| contents | Recent work that analyzed the effect of vacancy disorder on a short-range resonating valence bond spin liquid state of kagome-lattice antiferromagnets argued that such spin liquids are stable to vacancy disorder. The argument relied crucially on a numerical study that identified the following property of the site-diluted kagome lattice: maximum-density dimer packings (maximum matchings) of any connected component of such site-diluted kagome lattices have at most one unmatched vertex that hosts a monomer. Here, we provide an inductive proof of a stronger result that implies this property: If a connected cluster of such a lattice has an odd number of vertices, its Gallai-Edmonds decomposition~\cite{Lovas_Plummer_1986} has exactly one ${\mathcal R}$-type region that spans the entire connected cluster and hosts a single monomer of any maximum-density dimer packing. If on the other hand it has an even number of sites, it admits perfect matchings (fully-packed dimer coverings with no monomers) and its Gallai-Edmonds decomposition consists of a single ${\mathcal P}$-type region that spans the entire cluster. Our proof also applies to the site-diluted Archimedean star lattice, the site-diluted pyrochlore lattice (corner-sharing tetrahedra), the site-diluted hyperkagome lattice, and, more generally, to any lattice satisfying a certain local connectivity property. It does not apply to bond-diluted versions of such lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random geometry of maximum-density dimer packings of the site-diluted kagome lattice Bhola, Ritesh Damle, Kedar Disordered Systems and Neural Networks Recent work that analyzed the effect of vacancy disorder on a short-range resonating valence bond spin liquid state of kagome-lattice antiferromagnets argued that such spin liquids are stable to vacancy disorder. The argument relied crucially on a numerical study that identified the following property of the site-diluted kagome lattice: maximum-density dimer packings (maximum matchings) of any connected component of such site-diluted kagome lattices have at most one unmatched vertex that hosts a monomer. Here, we provide an inductive proof of a stronger result that implies this property: If a connected cluster of such a lattice has an odd number of vertices, its Gallai-Edmonds decomposition~\cite{Lovas_Plummer_1986} has exactly one ${\mathcal R}$-type region that spans the entire connected cluster and hosts a single monomer of any maximum-density dimer packing. If on the other hand it has an even number of sites, it admits perfect matchings (fully-packed dimer coverings with no monomers) and its Gallai-Edmonds decomposition consists of a single ${\mathcal P}$-type region that spans the entire cluster. Our proof also applies to the site-diluted Archimedean star lattice, the site-diluted pyrochlore lattice (corner-sharing tetrahedra), the site-diluted hyperkagome lattice, and, more generally, to any lattice satisfying a certain local connectivity property. It does not apply to bond-diluted versions of such lattices. |
| title | Random geometry of maximum-density dimer packings of the site-diluted kagome lattice |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2512.23639 |