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.

4.5 pages, 3 figures plus 9 pages supplemental material

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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