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arXiv · 2408.15699

Strongly interacting fermions are non-trivial yet non-glassy

Eric R. Anschuetz·Chi-Fang Chen·Bobak T. Kiani·Robbie King
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Abstract

Random spin systems at low temperatures are glassy and feature computational hardness in finding low-energy states. We study the random all-to-all interacting fermionic Sachdev--Ye--Kitaev (SYK) model and prove that, in contrast, (I) the low-energy states have polynomial circuit depth, yet (II) the annealed and quenched free energies agree to inverse-polynomially low temperatures, ruling out a glassy phase transition in this sense. These results are derived by showing that fermionic and spin systems significantly differ in their commutation index, which quantifies the non-commutativity of Hamiltonian terms. Our results suggest that low-temperature strongly interacting fermions, unlike spins, belong in a classically nontrivial yet quantumly easy phase.

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Eric R. Anschuetz, Chi-Fang Chen, Bobak T. Kiani, Robbie King. 2024-08-28. Strongly interacting fermions are non-trivial yet non-glassy. https://arxiv.org/abs/2408.15699

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