发表机构
University of Southern California; Bard College（南加州大学; 巴德学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究开放费米子系统中纠缠与负性谱的时间临界性，发现高斯性而非对称性决定临界性判据，并精确求解了Kitaev链中损耗、增益与退相干对临界性顺序和位置的影响。
AI 中文摘要
当纠缠谱或负性谱的两个最大本征值相遇时，相应的纠缠或负性哈密顿量的能隙闭合，而熵保持平滑，我们将此事件称为时间临界性。我们探究在开放费米子系统中此类临界性何时发生、以何种顺序出现，以及它们是否先于几何退相干时间（负性开始下降的时刻）。我们比较了仅平均意义上尊重费米子宇称（弱对称性）并保持态为高斯的损耗与增益，以及在每个跳跃中都尊重宇称（强对称性）并使态变为非高斯的密度退相干。我们发现，决定临界性判据的是高斯性而非对称性。在高斯态中，子系统的纠缠能隙恰好在其两个宇称扇区权重相等时闭合，而负性能隙恰好在该子系统或其补集满足此条件时闭合，因此负性临界性绝不会晚于纠缠临界性出现。均匀平衡的损耗与增益仅缩小两个宇称扇区的权重，并在任意速率下、对任意二次哈密顿量都保留两种临界性。在开放Kitaev链中，弱非平衡损耗与增益将临界性移动由切口处占据数决定的量，且在强速率下，仅当奇数个相邻位点经过半填充时，它们才允许在弛豫时间附近闭合。对于退相干，我们在链的键项对易的点上精确求解非高斯动力学。弱退相干延迟两种临界性，并且远离链端时，将它们移动到宇称平衡（高斯态的宇称规则会将其置于此处）之前。随着退相干速率接近临界阻尼，两种临界性都退回到无限时间，而在强退相干下，负性在任何能隙开始收缩之前很久就开始下降。
英文摘要
When the two largest eigenvalues of an entanglement or negativity spectrum meet, the gap of the corresponding entanglement or negativity Hamiltonian closes while entropies stay smooth, an event we call a temporal criticality. We ask when such criticalities occur in open fermionic systems, in which order, and whether they precede the geometric decoherence time, at which the negativity starts to fall. We compare loss and gain, which respect fermion parity only on average (weak symmetry) and keep the state Gaussian, with density dephasing, which respects it in every jump (strong symmetry) and makes the state non-Gaussian. We find that Gaussianity, rather than the symmetry, fixes the criterion for a criticality. In a Gaussian state the entanglement gap of a subsystem closes exactly when its two parity sectors carry equal weight, and the negativity gap closes exactly when this happens for the subsystem or its complement, so the negativity criticality never comes after the entanglement one. Uniform balanced loss and gain only shrink the two parities and leave both criticalities in place at every rate, for any quadratic Hamiltonian. In an open Kitaev chain, weak imbalanced loss and gain shift the criticalities by amounts set by the occupations at the cut, and at strong rates they allow a closing near the relaxation time only when an odd number of neighboring sites pass half filling. For dephasing we solve the non-Gaussian dynamics exactly at the point where the bond terms of the chain commute. Weak dephasing delays both criticalities and, away from the chain ends, moves them ahead of the parity balance, where the parity rules of Gaussian states would place them. As the dephasing rate approaches critical damping, both criticalities recede to infinite time, and at strong dephasing the negativity starts to fall long before either gap begins to shrink.
Comments27 + 36 pages, 5 + 3 figures, 1 + 5 tables
