Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany.
Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy and NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy.
Phys Rev Lett. 2019 Feb 1;122(4):040604. doi: 10.1103/PhysRevLett.122.040604.
We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.
我们提出了一种与量子多体系统中局部耗散杂质正交性灾难现象类似的现象。我们表明，当系统支持长程相关性时，保真度 F(t)，给出了从初始状态演化的时间的距离的度量，显示出一种普遍的标度形式 F(t)∝t^{θ}e^{-γt}，这与凝聚态物质中传统的正交性灾难实例相似。指数衰减率 γ 标志着环境退相干的开始，而保真度的附加代数贡献则极大地减缓了这种退相干。这个图像是在适合李雅普诺夫动力学的二阶累积量展开中推导出来的，并通过对一维横向场量子伊辛模型进行局部去相位跳跃算子、XY 和 XX 量子自旋链以及二维玻色气体在超流相中的局部粒子加热的验证得到了证实。我们的结果表明，局部耗散源可用于检查实时相关性并诱导开放量子多体系统中退相干的延迟。
