Matrix product state of multi-time correlations

Klobas, Katja; Vanicat, Matthieu; Garrahan, Juan P; Prosen, Tomaž

Abstract

For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of configurations observed along a time lattice. Such a time state is defined with respect to a particular equilibrium state that is invariant under space and time translations. The concept is developed within the rule 54 reversible cellular automaton, for which we explicitly construct a matrix product form of the time state, with matrices that act on the three-dimensional auxiliary space. We use the matrix-product state to express equal-space time-dependent density-density correlation function, which, for special maximum-entropy values of equilibrium parameters, agrees with the previous results. Additionally, we obtain an explicit expression for the probabilities of observing all multi-time configurations, which enables us to study distributions of times between consecutive excitations and prove the absence of decoupling of timescales in the rule 54 model.

• Journal Article Type: Article
• Acceptance Date: Apr 23, 2020
• Online Publication Date: Jul 29, 2020
• Publication Date: Aug 21, 2020
• Deposit Date: Oct 5, 2020
• Publicly Available Date: Jul 30, 2021
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 33
• Article Number: 335001
• DOI: https://doi.org/10.1088/1751-8121/ab8c62
• Keywords: Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/4940666
• Publisher URL: https://iopscience.iop.org/article/10.1088/1751-8121/ab8c62
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical . IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online athttps://doi.org/10.1088/1751-8121/ab8c62.