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Fredkin Staircase: An Integrable System with a Finite-Frequency Drude Peak
Hansveer Singh1, Romain Vasseur1, Sarang Gopalakrishnan2,3
1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Physical Review Letters
|February 10, 2023
Summary
We discovered the Fredkin staircase, a novel integrable cellular automaton with unique quasiparticles. This model exhibits diffusive charge transport and persistent current oscillations, revealing a Drude peak in its AC conductivity.
Area of Science:
- Physics
- Complex Systems
- Statistical Mechanics
Background:
- Integrable cellular automata are crucial for understanding complex systems.
- Existing models often fall into well-defined classifications.
- The Fredkin staircase presents a new structure beyond current classifications.
Purpose of the Study:
- Introduce and explore the Fredkin staircase, a novel interacting integrable cellular automaton.
- Investigate its unique properties and classification.
- Analyze its charge transport and conductivity.
Main Methods:
- Analytical construction of operators anticommuting with time-evolution.
- Investigation of quasiparticle behavior.
- Analysis of charge transport and AC conductivity.
Main Results:
- The Fredkin staircase possesses two families of ballistically propagating quasiparticles with infinite species.
- Despite ballistic quasiparticles, DC charge transport is diffusive with non-Gaussian dynamics.
- Persistent temporal current oscillations and a Drude peak in AC conductivity at nonzero frequency were observed.
Conclusions:
- The Fredkin staircase represents a new class of integrable models.
- Its unique properties, including the Drude peak, offer new insights into charge transport.
- The model's integrability is confirmed by the constructed anticommuting operators.
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