The Fredkin staircase: An integrable system with a finitefrequency 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 Bethesolvable 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 nongaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a deltafunction singularity (Drude peak) in the a.c. conductivity at nonzero frequency. We analytically construct an extensive set of operators that anticommute with the timeevolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lowerbound the weight of this finitefrequency singularity.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08542
 Bibcode:
 2022arXiv220508542S
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Quantum Physics
 EPrint:
 4.5 pages, 3 figures plus 9 pages supplemental material