Sharp universal death of entanglement threshold for Pauli Hamiltonians

Bobak T. Kiani

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arXiv · 2609.30149

Sharp universal death of entanglement threshold for Pauli Hamiltonians

Bobak T. Kiani

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Abstract

We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree $Δ\ge2$. 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 \[ β\le z_Δ:= \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{Δ-1} \right]. \] 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.

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Bobak T. Kiani. 2026-09-24. Sharp universal death of entanglement threshold for Pauli Hamiltonians. https://arxiv.org/abs/2609.30149

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