Fractal states of the Schwinger model
Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger model. Physical Review Letters. 132(5), 050401.
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Author
Petrova, ElenaISTA;
Tiunov, Egor S.;
Bañuls, Mari Carmen;
Fedorov, Aleksey K.
Department
Abstract
The lattice Schwinger model, the discrete version of QED in
1
+
1
dimensions, is a well-studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the self-similarity of the ground state, which allows us to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We present the results of recurrently calculating ground-state wave functions using the fractal Ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground-state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.
Publishing Year
Date Published
2024-01-30
Journal Title
Physical Review Letters
Publisher
American Physical Society
Acknowledgement
We thank A. Bargov, I. Khaymovich, and V. Tiunova for fruitful discussions and for useful comments. M. C. B. thanks S. Kühn for discussions about the phase structure of the model. A. K. F. thanks V. Gritsev and A. Garkun for insightful comments. E. V. P., E. S. T., and A. K. F. are
supported by the RSF Grant No. 20-42-05002 (studying the fractal Ansatz) and the Roadmap on Quantum Computing (Contract No. 868-1.3-15/15-2021, October 5, 2021; calculating on GS energies). A. K. F. thanks the Priority 2030 program at the NIST “MISIS” under the project No. K1-2022-027. M. C. B. was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868.
Volume
132
Issue
5
Article Number
050401
ISSN
eISSN
IST-REx-ID
Cite this
Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. Fractal states of the Schwinger model. Physical Review Letters. 2024;132(5). doi:10.1103/PhysRevLett.132.050401
Petrova, E., Tiunov, E. S., Bañuls, M. C., & Fedorov, A. K. (2024). Fractal states of the Schwinger model. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.132.050401
Petrova, Elena, Egor S. Tiunov, Mari Carmen Bañuls, and Aleksey K. Fedorov. “Fractal States of the Schwinger Model.” Physical Review Letters. American Physical Society, 2024. https://doi.org/10.1103/PhysRevLett.132.050401.
E. Petrova, E. S. Tiunov, M. C. Bañuls, and A. K. Fedorov, “Fractal states of the Schwinger model,” Physical Review Letters, vol. 132, no. 5. American Physical Society, 2024.
Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger model. Physical Review Letters. 132(5), 050401.
Petrova, Elena, et al. “Fractal States of the Schwinger Model.” Physical Review Letters, vol. 132, no. 5, 050401, American Physical Society, 2024, doi:10.1103/PhysRevLett.132.050401.
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