Ergodicity from Sachdev-Ye-Kitaev baths and ergodic inclusions

Sachdev-Ye-Kitaev 浴和遍历包含体的遍历性

• 批准号: 521308656
• 负责人: Professor Dr. Markus Philip Ludwig Heyl
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/521308656?language=en
• 关键词: Ergodicity; Sachdev; Ye; Kitaev; baths

Quantum baths play an important role in many parts of this Research Unit. Thermalization of isolated ultracold atomic gases can be understood by the system acting as its own bath. In many-body localized (MBL) systems the modeling of ergodic inclusions via a quantum bath can help to analyze the stability of the non-ergodic phase. Due to the general relevance of system plus bath settings, which long predate such current developments, a number of bath models have been developed. Two desirable features of such bath models can be in conflict: i) The bath model itself should be amenable to reliable analytical or numerical solutions without requiring too many computational resources. ii) The bath should provide a good description of the environment it is supposed to model. The most important bath models that fulfill the first requirement are a harmonic oscillator baths and the Lindblad formalism. However, in far-from-equilibrium situations it is not clear that the second criterion is also fulfilled: The bath should be a thermalizing system itself (ruling out harmonic oscillators) with nontrivial quantum coherence effects (ruling out Lindblad). In this research project we therefore analyze new models for quantum baths that can supplement the conventional approaches. One candidate is the Sachdev-Ye-Kitaev (SYK) model, which has recently generated a lot of excitement in condensed matter physics and in high-energy physics. It has the remarkable properties of being non-integrable and consistent with the eigenstate thermalization hypothesis, while still being analytically solvable. In view of the above desiderata this makes it an interesting bath model. The educated guess is that an SYK bath will be situated somewhere between harmonic oscillator baths and Lindblad formalism. One goal of this research project is to analyze the properties of such an SYK bath, especially in far-from-equilibrium situations. The second goal of this research project is to study ergodic inclusions in MBL systems. MBL challenges the traditional picture that interacting quantum many-body systems thermalize, and has therefore attracted a lot of attention. Understanding the behavior of ergodic inclusions is one route to analyze the stability of MBL phases. We will follow this route with various bath models, namely SYK baths, random unitary circuits (RUCs) and Floquet driving. All of these models show strong scrambling, RUCs can be implemented very efficiently numerically and Floquet driving is directly related to experiments in this Research Unit. Individually but especially taken together this will provide a better understanding of ergodic inclusions in MBL systems. We expect that this project will make a significant contribution towards a better understanding and modeling of quantum baths in far-from-equilibrium situations. Furthermore, it will provide a characterization of observable consequences of this modeling with an emphasis on ultracold atomic gases.

量子浴在该研究单元的许多地方都起着重要作用。孤立的超低原子气体的热化可以通过起作用的浴缸来理解。在多体局部（MBL）系统中，通过量子浴对麦芽胶合体的建模可以帮助分析非邻近相的稳定性。由于System Plus浴室设置的一般相关性（长期以来）早于此类发展，因此已经开发了许多浴室模型。此类浴室模型的两个理想特征可能会发生冲突：i）浴室模型本身应适合可靠的分析或数值解决方案，而无需过多的计算资源。 ii）浴缸应对其应建模的环境提供良好的描述。满足第一个需求的最重要的浴室模型是谐波振荡器浴和lindblad的形式主义。但是，在遥远的平衡情况下，尚不清楚第二个标准也可以满足：浴缸应是具有非平凡量子相干效应（排除Lindblad）的热化系统本身（排除谐波振荡器）。因此，在该研究项目中，我们分析了可以补充常规方法的量子浴的新模型。一个候选人是Sachdev-Ye-Kitaev（Syk）模型，该模型最近引起了凝结物理学和高能物理学的兴奋。它具有不可融合性的显着特性，并且与本征态热假说一致，同时仍可以在分析上解决。鉴于上述Desiderata，这使其成为一个有趣的浴室模型。受过良好教育的猜测是，Syk浴室将位于谐波振荡器浴和林德布拉德形式主义之间。该研究项目的目标之一是分析这种SYK浴的性质，尤其是在远程平衡情况下。该研究项目的第二个目标是研究MBL系统中的千古夹杂物。 MBL挑战了相互作用的量子多体系统的传统图片，因此吸引了很多关注。了解沿寿命夹杂物的行为是分析MBL相稳定性的一种途径。我们将采用各种浴室型号，即Syk浴室，随机统一电路（RUC）和Floquet驾驶。所有这些模型都表现出强烈的争夺，可以非常有效地实现RUC，而Floquet驱动器与本研究单元中的实验直接相关。单独但尤其是在一起，这将为MBL系统中的千古夹杂物提供更好的理解。我们预计该项目将在远程平衡情况下对量子浴的更好理解和建模做出重大贡献。此外，它将提供这种建模的可观察后果的特征，并强调超速原子气体。