Variational classical networks for dynamics in interacting quantum matter

• URL: http://arxiv.org/abs/2007.16084v2
• Date: Mon, 26 Apr 2021 18:00:06 GMT
• Title: Variational classical networks for dynamics in interacting quantum matter
• Authors: Roberto Verdel, Markus Schmitt, Yi-Ping Huang, Petr Karpov, and Markus Heyl
• Abstract summary: We introduce a variational class of wavefunctions based on complex networks of classical spins akin to artificial neural networks. We show that our method can be applied to any quantum many-body system with a well-defined classical limit.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 a 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 wavefunctions 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.

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