Claire Benjamin | Searcharxiv

arXiv2026

AKLT Hamiltonian from Hubbard tripods

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.

cond-mat.str-el↗

arXiv2024

DNA transport is topologically sculpted by active microtubule dynamics

The transport of macromolecules, such as DNA, through the cytoskeleton is critical to wide-ranging cellular processes from cytoplasmic streaming to transcription. The rigidity and steric hindrances imparted by the network of filaments comprising the cytoskeleton often leads to anomalous subdiffusion, while active processes such as motor-driven restructuring can induce athermal superdiffusion. Understanding the interplay between these seemingly antagonistic contributions to intracellular dynamics remains a grand challenge. Here, we use single-molecule tracking to show that the transport of large linear and circular DNA through motor-driven microtubule networks can be non-gaussian and multi-modal, with the degree and spatiotemporal scales over which these features manifest depending non-trivially on the state of activity and DNA topology. For example, active network restructuring increases caging and non-Gaussian transport modes of linear DNA, while dampening these mechanisms for rings. We further discover that circular DNA molecules exhibit either markedly enhanced subdiffusion or superdiffusion compared to their linear counterparts, in the absence or presence of kinesin activity, indicative of microtubules threading circular DNA. This strong coupling leads to both stalling and directed transport, providing a direct route towards parsing distinct contributions to transport and determining the impact of coupling on the transport signatures. More generally, leveraging macromolecular topology as a route to programming molecular interactions and transport dynamics is an elegant yet largely overlooked mechanism that cells may exploit for intracellular trafficking, streaming, and compartmentalization. This mechanism could be harnessed for the design of self-regulating, sensing, and reconfigurable biomimetic matter.

cond-mat.soft↗