Time-dependent matrix product ansatz for interacting reversible dynamics

Abstract

We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]. Our construction is based on an explicit solution of real-space real-time inverse scattering problem. We consider two applications of this tMPA. Firstly, we provide the first exact and explicit computation of the dynamic structure factor in an interacting deterministic model, and secondly, we solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these exact results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model, as expected for normal fluids.

arXiv comment39 pages

References in corpus (20)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Macroscopic fluctuation theory
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Hydrodynamic Diffusion in Integrable Systems
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Super-diffusion in one-dimensional quantum lattice models
• A geometric viewpoint on generalized hydrodynamics
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Fibonacci family of dynamical universality classes
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Diffusion in deterministic interacting lattice systems
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Integrability of a deterministic cellular automaton driven by stochastic boundaries
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Exactly solvable deterministic lattice model of crossover between ballistic and diffusive transport
• Exact matrix product decay modes of a boundary driven cellular automaton
• Two extensions of exact non-equilibrium steady states of a boundary driven cellular automaton
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

Cited by in corpus (40)

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• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
• Dynamics of charge fluctuations from asymmetric initial states
• Diffusion and operator entanglement spreading
• Integrable Matrix Models in Discrete Space-Time
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Exact solution of the Floquet-PXP cellular automaton
• Matrix product state of multi-time correlations
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Hierarchical generalization of dual unitarity
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
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• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Integrable deformations of superintegrable quantum circuits
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Integrability breaking in the Rule 54 cellular automaton
• Exact solution of the Rule 150 reversible cellular automaton
• Hopf algebras and solvable unitary circuits
• Exact results on the dynamics of the stochastic Floquet-East model
• On two reversible cellular automata with two particle species
• On two non-ergodic reversible cellular automata, one classical, the other quantum
• Operator spreading in quantum hardcore gases
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• Inhomogeneous MPA and exact steady states of boundary driven spin chains at large dissipation