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

TL;DR

The paper introduces the Fredkin staircase, an integrable cellular automaton with unique properties such as ballistic quasiparticles and a finite-frequency Drude peak, revealing novel transport phenomena beyond existing models.

Contribution

It presents a new integrable automaton outside known classifications, with multiple quasiparticle species and a finite-frequency Drude peak, expanding understanding of quantum transport.

Findings

Charge transport is diffusive despite ballistic quasiparticles.

The model exhibits persistent current oscillations.

A finite-frequency Drude peak is analytically demonstrated.

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.