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Variational classical networks for dynamics in interacting quantum matter

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Verdel,  Roberto
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Karpov,  Petr
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Heyl,  Markus
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Verdel, R., Schmitt, M., Huang, Y.-P., Karpov, P., & Heyl, M. (2021). Variational classical networks for dynamics in interacting quantum matter. Physical Review B, 103(16): 165103. doi:10.1103/PhysRevB.103.165103.


Cite as: https://hdl.handle.net/21.11116/0000-0008-9484-B
Abstract
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While remarkable progress has been witnessed in recent years for one-dimensional systems, much less has been achieved for interacting quantum models in higher dimensions, since they incorporate an additional layer of complexity. In this work, we employ a variational method that allows for an efficient and controlled computation of the dynamics of quantum many-body systems in one and higher dimensions. The approach presented here introduces a variational class of wave functions based on complex networks of classical spins akin to artificial neural networks, which can be constructed in a controlled fashion. We provide a detailed prescription for such constructions and illustrate their performance by studying quantum quenches in one- and two-dimensional models. In particular, we investigate the nonequilibrium dynamics of a genuinely interacting two-dimensional lattice gauge theory, the quantum link model, for which we have recently shown-employing the technique discussed thoroughly in this paper-that it features disorder-free localization dynamics [P. Karpov et al., Phys. Rev. Lett. 126, 130401 (2021)]. The present work not only supplies a framework to address purely theoretical questions but also could be used to provide a theoretical description of experiments in quantum simulators, which have recently seen an increased effort targeting two-dimensional geometries. Importantly, our method can be applied to any quantum many-body system with a well-defined classical limit.