Pauli 哈密顿量纠缠阈值的尖锐普适消亡
Sharp universal death of entanglement threshold for Pauli Hamiltonians
- Department of Computer Science, Bowdoin College（博多因学院计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文确定了有界度 Pauli 哈密顿量高温可分离性的精确普适阈值，并证明阈值之上存在纠缠 Gibbs 态，阈值之下可经典高效采样逼近。
AI中文摘要：
我们确定了有界度 $\Delta\ge2$ 的 Pauli 哈密顿量的精确普适高温可分离阈值。如果哈密顿量中每个系数的绝对值至多为 1，且每个项与至多 $\Delta$ 个其他项有重叠支撑，则当 $\beta \le z_\Delta:= \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{\Delta-1} \right]$ 时，Gibbs 态是乘积 Pauli 本征态的混合。对于每个 $\beta>z_\Delta$，一个最大重叠度至多 $\Delta$ 的有限交换哈密顿量具有纠缠的 Gibbs 态。在严格低于阈值的任何固定 $\beta<z_\Delta$ 处，经典多项式时间算法产生来自乘积 Pauli 本征态分布的样本，该分布在迹距离上逼近 Gibbs 态。
英文摘要：
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.
