AKLT Hamiltonian from Hubbard tripods
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912948814872576 |
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| author | Benjamin, Claire Varjas, Dániel Széchenyi, Gábor Romhányi, Judit Oroszlány, László |
| author_facet | Benjamin, Claire Varjas, Dániel Széchenyi, Gábor Romhányi, Judit Oroszlány, László |
| contents | We investigate how the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian can emerge from a microscopic fermionic model based on half-filled Hubbard tripods. We first show that a single tripod hosts a robust threefold-degenerate low-energy manifold corresponding to an effective $S = 1$ degree of freedom. This manifold prevails over a broad range of interactions and remains stable against moderate disorder. We then combine exact diagonalization with fourth-order quasi-degenerate perturbation theory to derive an effective bilinear-biquadratic spin model for a pair of coupled tripods and identify coupling regimes where the target ratio is approached. In particular, tuning leg-center hopping together with two symmetry-inequivalent leg-leg hoppings yields the characteristic singlet-triplet degeneracy associated with a biquadratic-to-bilinear ratio close to 1/3. Extending the analysis to three tripods, we compare nonequivalent coupling geometries and find a strategy that suppresses unwanted longer-range and multispin terms while preserving the target nearest-neighbor couplings in the weak-coupling regime. These results establish a concrete bottom-up route from Hubbard clusters to valence-bond-solid spin physics in tunable quantum-dot arrays. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | AKLT Hamiltonian from Hubbard tripods Benjamin, Claire Varjas, Dániel Széchenyi, Gábor Romhányi, Judit Oroszlány, László Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics We investigate how the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian can emerge from a microscopic fermionic model based on half-filled Hubbard tripods. We first show that a single tripod hosts a robust threefold-degenerate low-energy manifold corresponding to an effective $S = 1$ degree of freedom. This manifold prevails over a broad range of interactions and remains stable against moderate disorder. We then combine exact diagonalization with fourth-order quasi-degenerate perturbation theory to derive an effective bilinear-biquadratic spin model for a pair of coupled tripods and identify coupling regimes where the target ratio is approached. In particular, tuning leg-center hopping together with two symmetry-inequivalent leg-leg hoppings yields the characteristic singlet-triplet degeneracy associated with a biquadratic-to-bilinear ratio close to 1/3. Extending the analysis to three tripods, we compare nonequivalent coupling geometries and find a strategy that suppresses unwanted longer-range and multispin terms while preserving the target nearest-neighbor couplings in the weak-coupling regime. These results establish a concrete bottom-up route from Hubbard clusters to valence-bond-solid spin physics in tunable quantum-dot arrays. |
| title | AKLT Hamiltonian from Hubbard tripods |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2603.06455 |