PreprintCC BY 4.0arXiv
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 ≥ 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.
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BibTeX
@misc{bhattacharya2026parisi,
title = {{Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians}},
author = {Sohom Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20431},
eprint = {2609.20431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians
AU - Sohom Bhattacharya
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20431
UR - https://arxiv.org/abs/2609.20431
AB - 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 ≥ 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.
ER -