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This study identifies Rule 201, a deterministic variant of the Floquet-PXP model, as an exactly solvable instance where influence matrices remain finite-dimensional despite non-trivial interactions. By characterizing these matrices via matrix-product operators, the research provides exact analytical solutions for multi-time autocorrelation functions in large quantum many-body systems. This work advances the theoretical understanding of open quantum dynamics and integrable models relevant to quantum simulation and algorithm design.
Exact subsystem dynamics in the deterministic Floquet-PXP model
arXiv:2606.27337v2 Announce Type: replace-cross Abstract: The dynamics of local subsystems in a thermodynamically large quantum many-body system can be understood as effectively open as the system produces its own effective bath. The action of this bath can be characterised in terms of the so-called influence matrices. In generic situations, the complexity of these objects grows unfavourably with time, however, there exist solvable cases where influence matrices can be characterised exactly even in the presence of non-trivial interactions. Here we show that Rule 201, a deterministic version of the Floquet-PXP model, is one of these solvable instances. Indeed, it admits influence matrices given by a finite-dimensional matrix-product operator (MPO) that solves a finite set of algebraic conditions. We provide the solution, and characterise multi-time autocorrelation functions.
Abstract:The dynamics of local subsystems in a thermodynamically large quantum many-body system can be understood as effectively open as the system produces its own effective bath. The action of this bath can be characterised in terms of the so-called influence matrices. In generic situations, the complexity of these objects grows unfavourably with time, however, there exist solvable cases where influence matrices can be characterised exactly even in the presence of non-trivial interactions. Here we show that Rule 201, a deterministic version of the Floquet-PXP model, is one of these solvable instances. Indeed, it admits influence matrices given by a finite-dimensional matrix-product operator (MPO) that solves a finite set of algebraic conditions. We provide the solution, and characterise multi-time autocorrelation functions.
Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)
arXiv:2606.27337 [cond-mat.stat-mech]
(or arXiv:2606.27337v2 [cond-mat.stat-mech] for this version)
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