Exact subsystem dynamics in the deterministic Floquet-PXP model

• URL: http://arxiv.org/abs/2606.27337v1
• Date: Thu, 25 Jun 2026 17:46:33 GMT
• Title: Exact subsystem dynamics in the deterministic Floquet-PXP model
• Abstract summary: Rule 201 is a deterministic version of the Floquet-PXP model.<n>We provide the solution, and multi-time autocorrelation functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Solvable Quantum Circuits with non-Markovian Influence Matrices [0.13999481573773073]
  We propose a new systematic approach to generating quantum circuits with complex dynamics.<n>The resulting influence matrices are non-Markovian, exhibiting nontrivial temporal correlations.<n>We show that, contrary to previous solvable instances, these circuits produce patterns of correlations that closely resemble that of typical many-body systems.
  arXiv  Detail & Related papers  (2026-07-28T16:51:26Z)
• Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model [3.108119331549279]
  "Rule 201" quantum cellular automaton is an integrable Trotterization of the PXP Hamiltonian.<n>We develop local conditions called generalized zipper conditions that allow exact solutions of local dynamics.<n>This uncovers a rich landscape of nonequilibrium behavior exhibiting initial-state dependence.
  arXiv  Detail & Related papers  (2026-06-17T18:00:01Z)
• Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization [42.22857110018992]
  We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential.<n>We combine Hamiltonian-preserving schemes by Jin and Wen in Commun. Math. Sci. 3(3), 285-315 (2005) with the Schrdingerization method, which embeds the resulting nonunitary semi-discrete dynamics into a unitary Schrdinger type system.
  arXiv  Detail & Related papers  (2026-06-13T02:49:05Z)
• Tensor network influence functionals for open quantum systems with general Gaussian bosonic baths [0.0]
  We introduce a generalization to cases where the system is coupled to a single reservoir through multiple non-commuting operators.<n>We construct a Gaussian influence functional that properly handles Trotter errors arising from a finite evolution time step.<n>As a demonstration, we simulate the time evolution of driven two-level emitters coupled to a bosonic lattice at different lattice sites.
  arXiv  Detail & Related papers  (2026-03-24T17:00:07Z)
• Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learning [52.26396748560348]
  We provide an overview of high dimensional dynamical systems driven by random matrices.<n>We focus on applications to simple models of learning and generalization in machine learning theory.
  arXiv  Detail & Related papers  (2026-01-03T00:12:32Z)
• Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling [0.0]
  We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable.<n>We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point.<n>These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models.
  arXiv  Detail & Related papers  (2025-09-09T18:01:45Z)
• Decoherence time control by interconnection for finite-level quantum memory systems [0.7252027234425334]
  This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure. The Hamiltonian and the operators of coupling the system to the external bosonic fields depend linearly on the system variables. We consider the decoherence time over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution.
  arXiv  Detail & Related papers  (2023-11-04T01:21:55Z)
• Temporal Entanglement in Chaotic Quantum Circuits [62.997667081978825]
  The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. We show that temporal entanglement always follows a volume law in time. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.
  arXiv  Detail & Related papers  (2023-02-16T18:56:05Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)
• Influence matrix approach to many-body Floquet dynamics [0.0]
  We introduce an approach to study quantum many-body dynamics inspired by the Feynman-Vernon influence functional. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem.
  arXiv  Detail & Related papers  (2020-09-21T18:04:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.