Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians

Abstract:Quantum $p$-local spin glass Hamiltonians are natural quantum analogues of the classical spin glass models. We provide an asymptotic characterization of the maximal energy achievable by the product states. We prove that for every $p \ge 2$, the limit of ground state energy exists and is given by a Parisi-type variational formula. This settles a question left open by Anschuetz et. al. (2025). The variational formula also recovers the known large-$p$ asymptotics as a consequence. Finally, we prove that the limiting product state energy is universal for a broad class of non-Gaussian interactions.

Probability (math.PR); Quantum Physics (quant-ph)

arXiv:2609.20431 [math.PR]

(or arXiv:2609.20431v1 [math.PR] for this version)

https://doi.org/10.48550/arXiv.2609.20431 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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