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Projekt P8/2


Nonequilibrium Dynamics in 2D Clusters from the Perspective of Quantum Typicality and Eigenstate Thermalization


Robin SteinigewegJochen GemmerKristel Michielsen


Understanding fundamental aspects of the physics of many-body systems out of equilibrium is both, highly desired and notoriously difficult. In particular, explaining the occurrence of statistical behavior in isolated quantum systems continues to be a challenge to theory, including the derivation of omnipresent phenomena such as exponential relaxation, diffusion, equilibration, and thermalization from truly microscopic principles. Recent and substantial progress in this context is also related to the emergent concept of quantum typicality and the celebrated eigenstate thermalization hypothesis (ETH). While quantum typicality means in essence that an ensemble average is accurately given by an expectation value of just a single pure state drawn at random from a high-dimensional Hilbert space, the (diagonal part of the) ETH ansatz assumes such type of typicality even on the level of individual energy eigenstates.

In this project, we build on our previous works, e.g., on our works in the first funding period of this research unit, and plan to study nonequilibrium dynamics in two-dimensional (2D) clusters from the perspective of quantum typicality and ETH. In our study, we will heavily rely on the use of dynamical quantum typicality (DQT) and state-of-the-art (super) computing to tackle these 2D clusters, ranging from finite systems of interacting spins in a rectangular geometry, like two-leg or multi-leg ladders, to square lattices. Moreover, we will complement our analysis by a combination of DQT with projection operator techniques and numerical linked-cluster expansions (NCLE). Especially the latter combination of DQT with NLCE has the promising potential to shed light onto the physics of extended 2D models, with or without disorder. In this way, we might be able to contribute to the question of many-body localization in higher dimensions.

While a significant body of research in our project is devoted to transport quantities within the framework of linear response theory, another equally important question constitutes the role of the specific initial condition for the subsequent relaxation process. In this context, we will scrutinize our current proposal that the (off-diagonal part of the) ETH ansatz implies a "universal" relation between the dynamics far away from and close to equilibrium, by performing several cases studies beyond idealized models of random-matrix type. In the same context, our extension to observables of non-transport type also allows us to explore in how far typicality-based predictions for the entire relaxation process, essentially related to survival probabilities, apply to generic nonequilibrium situations.