Project Details
Projekt
Ergodicity from Sachdev-Ye-Kitaev baths and ergodic inclusions
Applicants
Professor Dr. Markus Philip Ludwig Heyl; Professor Dr. Stefan Kehrein; Professor Dr. Frank Pollmann
Subject Area
Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
Theoretical Condensed Matter Physics
Theoretical Condensed Matter Physics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 499180199
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.
DFG Programme
Research Units
