QMBDyn · Dynamical Phenomena in Quantum Many-Body Systems

Dynamical Phenomena in Quantum Many-Body Systems

Interactions between particles lead to a plethora of interesting phenomena such as magnetism or superconductivity and are a central theme of condensed matter physics. They are crucial for the process of thermalization, i.e. how a system may reach the thermodynamic equilibrium over the course of time if prepared in a nonequilibrium state. This fundamental question is increasingly attracting attention due to experimental and theoretical progress in the last decade, leading to a more detailed understanding. For isolated quantum systems, thermalization is particularly interesting since the notion of thermal equilibrium has to be generalized to local quantities, since the dynamics of the wave function in isolated systems precludes reaching a complete thermal state as described e.g. by the microcanonical ensemble. With this generalization, thermalization can be shown to exist in generic quantum systems, admiting an effective random matrix description. Surprisingly, it was recently found that there can be exceptions to thermalization in a class of generic strongly disordered interacting quantum systems due to the phenomenon of ``many-body localization'', a new dynamical nonequilibrium phase of matter. QMBDyn was devoted to the development of a better understanding of strongly interacting quantum many-body systems out of equilibrium and their thermalization process using numerically exact large methods and high performance computing to obtain unbiased results. The main results are: i) a computational confirmation of the analytical prediction that thermal inclusions may thermalize many-body localized systems with a large enough localization length; ii) the demonstration that generic periodically driven quantum many-body systems exhibit diffusive transport; iii) the construction of a new class of discrete time pseudo-crystals as a generic out of equilibrium state of matter; iv) the demonstration of anomalous thermalization in periodically driven disordered quantum many-body systems below critical disorder; v) the publication of a high performance open source code for the massively parallel shift-invert diagonalization of very large sparse matrices, along with a new computational record for the MBL problem; vi) the discovery of emergent locality in quantum many-body systems with long range interactions. Our work has multiple societal implications: Firstly, it is a contribution to fundamental science, paving the way to a deeper understanding of nonequilibrium quantum systems and how thermal equilibrium is reached. Secondly, our results provide important verifications of recently discovered new stroboscopic thermodynamic ensembles in periodically driven quantum systems. Thirdly, our computational work pushes significantly the state of the art for the calculation of exact central eigenpairs of large sparse matrices as they occur in the many body problem. This is an important incentive for the further optimization and use of powerful massively parallel open source codes such as MUMPS and STRUMPACK, which will benefit both science and industry.

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