Matrix product state of multi-time correlations

Journal article

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.

Authors: Klobas, K; Vanicat, M; Garrahan, JP; Prosen, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Science
• Journal: https://iopscience.iop.org/journal/1751-8121
• Volume: 53
• Issue: 33
• Article number: 335001
• Publication date: 2020-08-21
• Acceptance date: 2020-04-23
• DOI: 10.1088/1751-8121/ab8c62
• EISSN: 1751-8121
• ISSN: 1751-8113
• Language: English
• Keywords: cellular automata; exact results; FFR; solvable lattice models; multi-time correlations; matrix product ansatz