Time-dependent Neural Galerkin Method for Quantum Dynamics

• URL: http://arxiv.org/abs/2412.11778v1
• Date: Mon, 16 Dec 2024 13:48:54 GMT
• Title: Time-dependent Neural Galerkin Method for Quantum Dynamics
• Authors: Alessandro Sinibaldi, Douglas Hendry, Filippo Vicentini, Giuseppe Carleo,
• Abstract summary: We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
• Score: 42.81677042059531
• License:
• Abstract: We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time window by minimizing a physically motivated loss function that enforces the Schr\"odinger's equation. The variational state is parametrized with a Galerkin-inspired ansatz based on a time-dependent linear combination of time-independent Neural Quantum States. This structure effectively captures the relevant dynamical frequencies in the time evolution and is particularly well-suited for exploring long-time dynamics. We showcase the method's effectiveness by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. By extracting the asymptotic long-time evolution, we uncover signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches and highlight the potential to explore previously inaccessible dynamical regimes of strongly interacting quantum systems.

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