Strongly interacting fermions are non-trivial yet non-glassy
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.
Cite
@article{arxiv.2408.15699,
title = {Strongly interacting fermions are non-trivial yet non-glassy},
author = {Eric R. Anschuetz and Chi-Fang Chen and Bobak T. Kiani and Robbie King},
journal= {arXiv preprint arXiv:2408.15699},
year = {2024}
}
Comments
New result on commutation index of k-local Paulis for k > log(n)