A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton
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 i...
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2025-02-01
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| author | Alessandro Bisio Paolo Perinotti Andrea Pizzamiglio Saverio Rota |
| author_facet | Alessandro Bisio Paolo Perinotti Andrea Pizzamiglio Saverio Rota |
| author_sort | Alessandro Bisio |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0ce7d26eafc947b59f4daa15290ebae5 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-0ce7d26eafc947b59f4daa15290ebae52025-08-20T03:12:11ZengMDPI AGEntropy1099-43002025-02-0127219810.3390/e27020198A Perturbative Approach to the Solution of the Thirring Quantum Cellular AutomatonAlessandro Bisio0Paolo Perinotti1Andrea Pizzamiglio2Saverio Rota3Dipartimento di Fisica, Università di Pavia, 27100 Pavia, ItalyDipartimento di Fisica, Università di Pavia, 27100 Pavia, ItalyDipartimento di Fisica, Università di Pavia, 27100 Pavia, ItalyDipartimento di Fisica, Università di Pavia, 27100 Pavia, ItalyThe 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.https://www.mdpi.com/1099-4300/27/2/198quantum cellular automataThirring quantum cellular automatonpath sum solutionperturbative approach |
| spellingShingle | Alessandro Bisio Paolo Perinotti Andrea Pizzamiglio Saverio Rota A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton Entropy quantum cellular automata Thirring quantum cellular automaton path sum solution perturbative approach |
| title | A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton |
| title_full | A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton |
| title_fullStr | A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton |
| title_full_unstemmed | A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton |
| title_short | A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton |
| title_sort | perturbative approach to the solution of the thirring quantum cellular automaton |
| topic | quantum cellular automata Thirring quantum cellular automaton path sum solution perturbative approach |
| url | https://www.mdpi.com/1099-4300/27/2/198 |
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