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Alessandro Bisio1, Giacomo Mauro D'Ariano1, Nicola Mosco1

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Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

We explored solutions for an interacting Fermionic cellular automaton, a discrete analogue of the Thirring model. This study reveals unique scattering and bound states, differing significantly from traditional Hamiltonian systems.

Keywords:
Hubbard modelThirring modelquantum walks

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The Thirring model is a fundamental quantum field theory describing interacting fermions.
  • Cellular automata offer discrete analogues for studying complex physical systems.
  • Understanding interacting many-body systems is crucial in quantum physics.

Purpose of the Study:

  • To derive and analyze two-particle solutions for an interacting Fermionic cellular automaton.
  • To investigate the unique scattering and bound-state properties of this discrete model.
  • To compare the automaton's behavior with its continuous Hamiltonian counterpart, the Thirring model.

Main Methods:

  • Exploiting symmetries of the evolution operator for analytical derivation.
  • Analyzing a two-step evolution operator: unitary interaction and independent Dirac quantum walks.
  • Complementing analytical findings with numerical simulations of the interacting evolution.

Main Results:

  • The automaton exhibits scattering solutions with non-trivial momentum transfer, leading to Fermion-doubled particles.
  • Unlike Hamiltonian systems, bound states exist for all total momentum and coupling constant values.
  • Even with vanishing coupling, bound states appear at specific total momentum values.

Conclusions:

  • The interacting Fermionic cellular automaton presents distinct quantum phenomena compared to continuous models.
  • The discrete nature allows for novel particle behaviors like Fermion-doubling and universal bound states.
  • This model serves as a valuable discrete analogue for exploring complex fermionic interactions.