Matrix product state of multi-time correlations

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 3-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.

arXiv comment17 pages, 3 figures

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• Integrable Matrix Models in Discrete Space-Time
• Exact solution of the Floquet-PXP cellular automaton
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Space-like dynamics in a reversible cellular automaton
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• Exact solution of the Rule 150 reversible cellular automaton
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Quantum turnstiles for robust measurement of full counting statistics
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• Operator spreading in quantum hardcore gases
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