Optimal Sampling of Dynamical Large Deviations in Two Dimensions via Tensor Networks

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

Abstract

We use projected entangled-pair states (PEPS) to calculate the large deviation statistics of the dynamical activity of the two-dimensional East model, and the two-dimensional symmetric simple exclusion process (SSEP) with open boundaries, in lattices of up to 40×40 sites. We show that at long times both models have phase transitions between active and inactive dynamical phases. For the 2D East model we find that this trajectory transition is of the first order, while for the SSEP we find indications of a second order transition. We then show how the PEPS can be used to implement a trajectory sampling scheme capable of directly accessing rare trajectories. We also discuss how the methods described here can be extended to study rare events at finite times.

Citation

Causer, L., Bañuls, M. C., & Garrahan, J. P. (2023). Optimal Sampling of Dynamical Large Deviations in Two Dimensions via Tensor Networks. Physical Review Letters, 130(14), Article 147401. https://doi.org/10.1103/PhysRevLett.130.147401

• Journal Article Type: Article
• Acceptance Date: Mar 20, 2023
• Online Publication Date: Apr 4, 2023
• Publication Date: Apr 7, 2023
• Deposit Date: Mar 21, 2023
• Publicly Available Date: Apr 4, 2023
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 14
• Article Number: 147401
• DOI: https://doi.org/10.1103/PhysRevLett.130.147401
• Keywords: First order phase transitions; second order phase transitions; exclusion processes; glasses; finite-size scaling; large deviation & rare event statistics; Monte Carlo methods; projected entangled pair states; tensor network methods
• Public URL: https://nottingham-repository.worktribe.com/output/18808038
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.147401