Many-body dynamics with explicitly time-dependent neural quantum states

• URL: http://arxiv.org/abs/2412.11830v1
• Date: Mon, 16 Dec 2024 14:53:26 GMT
• Title: Many-body dynamics with explicitly time-dependent neural quantum states
• Authors: Anka Van de Walle, Markus Schmitt, Annabelle Bohrdt,
• Abstract summary: We introduce the time-dependent neural quantum state (t-NQS) We optimize a single, time-independent set of parameters to solve the time-dependent Schr"odinger equation across an entire time interval. Results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.
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• Abstract: Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions, but their application to time evolution faces scaling challenges. We introduce the time-dependent neural quantum state (t-NQS), a novel approach incorporating explicit time dependence into the neural network ansatz. This framework optimizes a single, time-independent set of parameters to solve the time-dependent Schr\"odinger equation across an entire time interval. We detail an autoregressive, attention-based transformer architecture and techniques for extending the model's applicability. To benchmark and demonstrate our method, we simulate quench dynamics in the 2D transverse field Ising model and the time-dependent preparation of the 2D antiferromagnetic state in a Heisenberg model, demonstrating state of the art performance, scalability, and extrapolation to unseen intervals. These results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.

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