Matrix product state of multi-time correlations

Katja Klobas*, Matthieu Vanicat, Juan P. Garrahan, Tomaž Prosen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number335001
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number33
DOIs
Publication statusPublished - 21 Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd.

Keywords

  • cellular automata
  • exact results
  • matrix product ansatz
  • multi-time correlations
  • solvable lattice models

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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