耗散量子多体系统的随机性突变
Orthogonality catastrophe in dissipative quantum many body systems
摘要：
我们提出了一个模拟的正交性突变现象的量子多体系统受到局部耗散杂质。我们表明，保真度$F(t)$，给出一个衡量的时间演化状态从初始的距离，显示一个通用的缩放形式$F(t)\propto t^θe^{-γt}$，当系统支持远程相关性，在凝聚态的正交性灾难的传统实例的方式让人想起。以速率$γ$的指数下降表示环境退相干的开始，其被对保真度的额外代数贡献严重减慢。这幅图是在一个适合于Liouvillian动力学的二阶累积展开中导出的，并对受局部退相跳跃算子约束的一维横向场量子伊辛模型、XY和XX量子自旋链以及局部粒子加热的超流相深处的二维玻色气体进行了证实。我们的结果表明，在开放量子多体系统中，局域耗散源可以用来检测实时关联和诱导退相干延迟。
英文摘要：
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 $F(t)\propto t^θe^{-γt}$, when the system supports long range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential fall-off 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.
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