A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Computational Physics

Background:

• The Thirring Quantum Cellular Automaton (QCA) models discrete fermionic dynamics.
• It serves as a quantum cellular automaton counterpart to the Thirring model in quantum field theory.

Purpose of the Study:

• To develop and apply perturbative techniques for the Thirring QCA path sum approach.
• To compute transition amplitudes in two- and three-particle sectors for varying mass parameters and interaction vertices.

Main Methods:

• Perturbative expansion of interaction vertices and mass parameter in the Thirring QCA.
• Classification of paths in regimes of very light and very heavy particles.
• Calculation of transition amplitudes in specific particle sectors.

Main Results:

• Successfully computed transition amplitudes to the first few orders for two- and three-particle sectors.
• Demonstrated the applicability of the developed techniques to the many-particle sector.
• Addressed the combinatorial complexity inherent in QCA path sum calculations.

Conclusions:

• The developed perturbative techniques offer a viable method for analyzing the Thirring QCA.
• The findings provide insights into the behavior of many-particle systems with on-site number-preserving interactions in one spatial dimension.