Work

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

Year: 2025

Type: article

Abstract: The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton, followed by the most general on-site number-preserving interaction, and serves as the QCA counterpart of the Thirring model in quantum field theory. In this work, we develop perturbative techniques for the QCA path sum approach, expanding both the number of interaction vertices and the mass parameter of the Thirring QCA. By classifying paths within the regimes of very light and very heavy particles, we computed the transition amplitudes in the two- and three-particle sectors to the first few orders. Our investigation into the properties of the Thirring QCA, addressing the combinatorial complexity of the problem, yielded some useful results applicable to the many-particle sector of any on-site number-preserving interactions in one spatial dimension.

Source: Entropy

DOI: 10.3390/e27020198

Authors: Alessandro Bisio, Paolo Perinotti, Andrea Pizzamiglio, Saverio Rota

Institutions: University of Pavia, Istituto Nazionale di Fisica Nucleare, Sezione di Pavia

Language: English

Topic: Cellular Automata and Applications

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: European Commission, Ministero dell'Università e della Ricerca