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Integrable spin chains and cellular automata with medium-range interaction.

Tamás Gombor1,2, Balázs Pozsgay1

  • 1MTA-ELTE "Momentum" Integrable Quantum Dynamics Research Group, Department of Theoretical Physics, Eötvös Loránd University, 1117 Budapest, Hungary.

Physical Review. E
|December 24, 2021
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Summary
This summary is machine-generated.

Researchers developed a new algebraic framework for integrable spin chains and cellular automata with medium-range interactions. This framework classifies new integrable models, including quantum deformations of classical cellular automata like Rule105 and Rule150.

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Area of Science:

  • Theoretical physics
  • Quantum mechanics
  • Statistical mechanics

Background:

  • Integrable spin chains and cellular automata are crucial in quantum and classical physics.
  • Existing theories primarily focus on nearest-neighbor interactions, leaving medium-range models under-explored.
  • A general theory for integrable models with interaction range ℓ≥3 was lacking.

Purpose of the Study:

  • To develop a general algebraic framework for integrable spin chains and cellular automata with medium-range interactions (ℓ≥3).
  • To establish a new integrability condition for classifying these medium-range models.
  • To identify and classify new integrable models, including applications in quantum brickwork circuits.

Main Methods:

  • Generalization of algebraic methods from nearest-neighbor interacting chains to medium-range interactions.
  • Development of a new integrability condition for medium-range Hamiltonians.
  • Classification of U(1)-symmetric three-site interacting models and interaction-round-a-face relevant Hamiltonians.
  • Analysis of quantum brickwork circuits and their relation to classical cellular automata.

Main Results:

  • A novel algebraic framework and integrability condition for medium-range integrable models were established.
  • Several new integrable models were identified, including integrable quantum deformations of classical cellular automata Rule105 and Rule150.
  • The Rule105 and Rule150 models were shown to be Yang-Baxter integrable with three-site interactions.
  • The famous Rule54 model was found not to belong to the family of integrable three-site models.

Conclusions:

  • The developed framework successfully classifies integrable models with medium-range interactions, filling a significant theoretical gap.
  • The findings provide new integrable quantum deformations and conserved charges for specific cellular automata models.
  • The study highlights the applicability of the framework to quantum brickwork circuits and sheds light on the integrability of classical cellular automata.