AKLT Hamiltonian from Hubbard tripods

TL;DR

This paper demonstrates how the AKLT spin-1 Hamiltonian can be derived from a microscopic Hubbard model using tripods, combining numerical and perturbative methods to connect fermionic clusters with valence-bond-solid physics.

Contribution

It provides a detailed microscopic derivation of the AKLT Hamiltonian from Hubbard tripods and explores coupling regimes for experimental realization.

Findings

Robust threefold-degenerate low-energy manifold in a single tripod

Effective bilinear-biquadratic spin model derived from coupled tripods

Strategies to suppress unwanted interactions in tripod arrays

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.