Time-dependent Neural Galerkin Method for Quantum Dynamics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908990331420672 |
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| author | Sinibaldi, Alessandro Hendry, Douglas Vicentini, Filippo Carleo, Giuseppe |
| author_facet | Sinibaldi, Alessandro Hendry, Douglas Vicentini, Filippo Carleo, Giuseppe |
| contents | 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 loss function that enforces the Schrödinger'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 is particularly well-suited for exploring long-time dynamics and enables bounding the error with the exact evolution via the global loss function. We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D, uncovering signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, our method is competitive compared to state-of-the-art time-dependent variational approaches, while unlocking previously inaccessible dynamical regimes of strongly interacting quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-dependent Neural Galerkin Method for Quantum Dynamics Sinibaldi, Alessandro Hendry, Douglas Vicentini, Filippo Carleo, Giuseppe Quantum Physics Other Condensed Matter Computational Physics 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 loss function that enforces the Schrödinger'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 is particularly well-suited for exploring long-time dynamics and enables bounding the error with the exact evolution via the global loss function. We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D, uncovering signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, our method is competitive compared to state-of-the-art time-dependent variational approaches, while unlocking previously inaccessible dynamical regimes of strongly interacting quantum systems. |
| title | Time-dependent Neural Galerkin Method for Quantum Dynamics |
| topic | Quantum Physics Other Condensed Matter Computational Physics |
| url | https://arxiv.org/abs/2412.11778 |