Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915723815682048 |
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| author | Kránitz, Péter Penc, Karlo |
| author_facet | Kránitz, Péter Penc, Karlo |
| contents | We construct rigorous Anderson-type lower bounds on the ground-state energy of the spin-$S$ Heisenberg antiferromagnet on the pyrochlore lattice. By formulating and optimizing a hierarchy of local cluster motifs ordered by size, we generate a sequence of increasingly tight bounds. A seven-site "hourglass" cluster composed of two corner-sharing tetrahedra furnishes an optimal lower bound that admits a closed-form expression for arbitrary spin $S$. We also derive exact lower bounds for generalized models with further-neighbor exchange, ring exchange, and scalar spin-chirality interactions. For $S=1/2$ and $S=1$, numerical optimization of an 18-site "crown" cluster containing a hexagonal loop yields rigorous lower bounds on the ground-state energy per site of the nearest-neighbor Heisenberg model with unit exchange, $e_\mathrm{GS} \geq -0.549832$ and $e_\mathrm{GS} \geq -1.632985$, respectively. We compare the resulting bounds with numerical ground-state energy estimates from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07800 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet Kránitz, Péter Penc, Karlo Strongly Correlated Electrons We construct rigorous Anderson-type lower bounds on the ground-state energy of the spin-$S$ Heisenberg antiferromagnet on the pyrochlore lattice. By formulating and optimizing a hierarchy of local cluster motifs ordered by size, we generate a sequence of increasingly tight bounds. A seven-site "hourglass" cluster composed of two corner-sharing tetrahedra furnishes an optimal lower bound that admits a closed-form expression for arbitrary spin $S$. We also derive exact lower bounds for generalized models with further-neighbor exchange, ring exchange, and scalar spin-chirality interactions. For $S=1/2$ and $S=1$, numerical optimization of an 18-site "crown" cluster containing a hexagonal loop yields rigorous lower bounds on the ground-state energy per site of the nearest-neighbor Heisenberg model with unit exchange, $e_\mathrm{GS} \geq -0.549832$ and $e_\mathrm{GS} \geq -1.632985$, respectively. We compare the resulting bounds with numerical ground-state energy estimates from the literature. |
| title | Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.07800 |