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Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
Physical Review Letters ( IF 8.6 ) Pub Date : 2022-11-23 , DOI: 10.1103/physrevlett.129.220602 Elias Starchl 1 , Lukas M Sieberer 1
Physical Review Letters ( IF 8.6 ) Pub Date : 2022-11-23 , DOI: 10.1103/physrevlett.129.220602 Elias Starchl 1 , Lukas M Sieberer 1
Affiliation
The construction of the generalized Gibbs ensemble, to which isolated integrable quantum many-body systems relax after a quantum quench, is based upon the principle of maximum entropy. In contrast, there are no universal and model-independent laws that govern the relaxation dynamics and stationary states of open quantum systems, which are subjected to Markovian drive and dissipation. Yet, as we show, relaxation of driven-dissipative systems after a quantum quench can, in fact, be determined by a maximum entropy ensemble, if the Liouvillian that generates the dynamics of the system has parity-time symmetry. Focusing on the specific example of a driven-dissipative Kitaev chain, we show that, similar to isolated integrable systems, the approach to a parity-time symmetric generalized Gibbs ensemble becomes manifest in the relaxation of local observables and the dynamics of subsystem entropies. In contrast, the directional pumping of fermion parity, which is induced by nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon that is unique to relaxation dynamics in driven-dissipative systems. Upon increasing the strength of dissipation, parity-time symmetry is broken at a finite critical value, which thus constitutes a sharp dynamical transition that delimits the applicability of the principle of maximum entropy. We show that these results, which we obtain for the specific example of the Kitaev chain, apply to broad classes of noninteracting fermionic models, and we discuss their generalization to a noninteracting bosonic model and an interacting spin chain.
中文翻译:
驱动耗散 Kitaev 链中量子淬火后奇偶校验时间对称广义吉布斯系综的弛豫
广义吉布斯系综的构建基于最大熵原理,孤立的可积量子多体系统在量子猝灭后弛豫到该系综。相比之下,没有普遍的和模型无关的定律来控制开放量子系统的弛豫动力学和静止状态,这些系统受到马尔可夫驱动和耗散的影响。然而,正如我们所展示的,如果产生系统动力学的 Liouvillian 具有宇称时间对称性,那么量子猝灭后驱动耗散系统的弛豫实际上可以由最大熵系综确定。着眼于驱动耗散 Kitaev 链的具体示例,我们表明,类似于孤立的可积系统,宇称时间对称广义吉布斯系综的方法在局部可观测值的弛豫和子系统熵的动力学中变得明显。相比之下,由 Kitaev 链的非平凡非厄米拓扑引起的费米子宇称的定向泵浦代表了驱动耗散系统中弛豫动力学所特有的现象。随着耗散强度的增加,宇称时间对称性在有限临界值处被打破,因此构成了一个急剧的动力学转变,限制了最大熵原理的适用性。我们表明,我们针对 Kitaev 链的具体示例获得的这些结果适用于广泛类别的非相互作用费米子模型,
更新日期:2022-11-23
中文翻译:
驱动耗散 Kitaev 链中量子淬火后奇偶校验时间对称广义吉布斯系综的弛豫
广义吉布斯系综的构建基于最大熵原理,孤立的可积量子多体系统在量子猝灭后弛豫到该系综。相比之下,没有普遍的和模型无关的定律来控制开放量子系统的弛豫动力学和静止状态,这些系统受到马尔可夫驱动和耗散的影响。然而,正如我们所展示的,如果产生系统动力学的 Liouvillian 具有宇称时间对称性,那么量子猝灭后驱动耗散系统的弛豫实际上可以由最大熵系综确定。着眼于驱动耗散 Kitaev 链的具体示例,我们表明,类似于孤立的可积系统,宇称时间对称广义吉布斯系综的方法在局部可观测值的弛豫和子系统熵的动力学中变得明显。相比之下,由 Kitaev 链的非平凡非厄米拓扑引起的费米子宇称的定向泵浦代表了驱动耗散系统中弛豫动力学所特有的现象。随着耗散强度的增加,宇称时间对称性在有限临界值处被打破,因此构成了一个急剧的动力学转变,限制了最大熵原理的适用性。我们表明,我们针对 Kitaev 链的具体示例获得的这些结果适用于广泛类别的非相互作用费米子模型,