The Fredkin staircase: An integrable system with a finite-frequency Drude peak

Abstract

We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the d.c. limit, albeit with a highly non-gaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the a.c. conductivity at nonzero frequency. We analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower-bound the weight of this finite-frequency singularity.

arXiv comment4.5 pages, 3 figures plus 9 pages supplemental material

References in corpus (51)

• The density-matrix renormalization group in the age of matrix product states
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Glassy dynamics of kinetically constrained models
• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Saturation of electrical resistivity
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Finite-temperature transport in one-dimensional quantum lattice models
• The transient localization scenario for charge transport in crystalline organic materials
• Hydrodynamic Diffusion in Integrable Systems
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Fracton hydrodynamics
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Finite automata for caching in matrix product algorithms
• Kinetically constrained freezing transition in a dipole-conserving system
• Superdiffusion in spin chains
• Power law violation of the area law in quantum spin chains
• Anomalous Subdiffusion from Subsystem Symmetries
• The isolated Heisenberg magnet as a quantum time crystal
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Diffusion in deterministic interacting lattice systems
• Bad Metals from Fluctuating Density Waves
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
• Integrable many-body quantum Floquet-Thouless pumps
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Deformed Fredkin Spin Chain with Extensive Entanglement
• Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains
• Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
• Nonergodic Quantum Dynamics from Deformations of Classical Cellular Automata
• Bad-Metallic Behavior of Doped Mott Insulators
• Quantum spin chains with multiple dynamics
• Anomalous optical absorption in overdoped cuprates near the charge-ordering instability
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Exact solution of the Floquet-PXP cellular automaton
• Quantum butterfly effect in polarized Floquet systems
• Displaced Drude peak and bad metal from the interaction with slow fluctuations
• Out-of-Time-Ordered Crystals and Fragmentation
• Entropy, gap and a multi-parameter deformation of the Fredkin spin chain
• Finite-size Gap, Magnetization, and Entanglement of Deformed Fredkin Spin Chain
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Emergent kinetic constraints in open quantum systems
• Revisiting the Mazur bound and the Suzuki equality
• Exact solution of the Rule 150 reversible cellular automaton
• Slow dynamics of the Fredkin spin chain
• Anti-Drude Metal of Bosons

Cited by in corpus (8)

• Solvable model of deep thermalization with distinct design times
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Open-system spin transport and operator weight dissipation in spin chains
• Subdiffusive transport in the Fredkin dynamical universality class
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Symmetries of the periodic Fredkin chain
• Absence of local conserved charges of the Fredkin spin chain and its truncated versions