Optimal sampling of dynamical large deviations via matrix product states

Causer, Luke; Bañuls, Mari Carmen; Garrahan, Juan P.

Abstract

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

Citation

Causer, L., Bañuls, M. C., & Garrahan, J. P. (2021). Optimal sampling of dynamical large deviations via matrix product states. Physical Review E, 103(6), Article 062144. https://doi.org/10.1103/PhysRevE.103.062144

• Journal Article Type: Article
• Acceptance Date: May 7, 2021
• Online Publication Date: Jun 28, 2021
• Publication Date: Jun 1, 2021
• Deposit Date: Jul 22, 2021
• Publicly Available Date: Jul 22, 2021
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 103
• Issue: 6
• Article Number: 062144
• DOI: https://doi.org/10.1103/PhysRevE.103.062144
• Public URL: https://nottingham-repository.worktribe.com/output/5814895
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.062144
• Additional Information: ©2021 American Physical Society