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Sharp universal death of entanglement threshold for Pauli Hamiltonians
Abstract
We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree Δ≥2. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most Δ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever β≤ zΔ:= arctanh[max0≤ x ≤ 1x((1−x)/(1+x))Δ−1 ]. For every β>zΔ, a finite commuting Hamiltonian with maximum overlap degree at most Δ has an entangled Gibbs state. At any fixed β<zΔ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.
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BibTeX
@misc{kiani2026sharp,
title = {{Sharp universal death of entanglement threshold for Pauli Hamiltonians}},
author = {Bobak T. Kiani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30149},
eprint = {2609.30149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30149},
}
RIS
TY - UNPB
TI - Sharp universal death of entanglement threshold for Pauli Hamiltonians
AU - Bobak T. Kiani
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30149
UR - https://arxiv.org/abs/2609.30149
AB - We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree Δ≥2. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most Δ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever β≤ z_Δ:= arctanh[max_0≤ x ≤ 1x((1−x)/(1+x))^Δ−1 ]. For every β>z_Δ, a finite commuting Hamiltonian with maximum overlap degree at most Δ has an entangled Gibbs state. At any fixed β<z_Δ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.
ER -