AKLT Hamiltonian from Hubbard tripods

• URL: http://arxiv.org/abs/2603.06455v1
• Date: Fri, 06 Mar 2026 16:46:07 GMT
• Title: AKLT Hamiltonian from Hubbard tripods
• Abstract summary: We first show that a single tripod hosts a robust threefold-degenerate low-energy manifold corresponding to an effective $S = 1$ degree of freedom.<n>We then combine exact diagonalization with fourth-order quasi-degenerate theory to derive an effective bilinear-biquadratic spin model for a pair of coupled tripods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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