Solutions of a Two-Particle Interacting Quantum Walk

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.