标题： 对称性在高温下强制纠缠 显示英文标题

标题： Symmetry enforces entanglement at high temperatures

摘要： 多体量子系统在局部相互作用下在高温下会发生“纠缠的突然死亡”，此时热态变为乘积态的经典混合态。我们研究对称性约束是否可以防止这一现象。我们证明，在对称性作用和强对称性的电荷子空间满足温和条件的情况下，具有位点阿贝尔对称性的通用哈密顿量的强对称热态（规范系综）在任意高温下仍保持非零的纠缠负性。我们的结果扩展到弱对称热态（吉布斯系综）在选择规则下的情况，这些规则限制状态分解为对称的。特别是，我们表明费米吉布斯态不会表现出纠缠的突然死亡，并且在高温下具有持续的费米纠缠负性。这些发现表明，全局对称性关联可以在热退相干的情况下保持量子纠缠，为对称性与热平衡中量子信息之间的相互作用提供了新的见解。 显示英文摘要

摘要： Many-body quantum systems with local interactions undergo "sudden death of entanglement" at high temperatures, whereby thermal states become classical mixtures of product states. We investigate whether symmetry constraints can prevent this phenomenon. We prove that strongly symmetric thermal states (canonical ensemble) of generic Hamiltonians with on-site Abelian symmetries remain entangled with non-zero entanglement negativity at arbitrarily high temperatures, under mild conditions on the symmetry actions and the charge sector of the strong symmetry. Our results extend to weakly symmetric thermal states (Gibbs ensemble) under superselection rules, which restrict state decompositions to be symmetric. In particular, we show that fermionic Gibbs states do not exhibit sudden death of entanglement and have persistent fermionic negativity at high temperatures. These findings demonstrate that global symmetry correlations can preserve quantum entanglement despite thermal decoherence, providing new insights into the interplay between symmetry and quantum information in thermal equilibrium.