article published yes Elena Petrova author 0ac84990-897b-11ed-a09c-f5abb56a4ede Egor S. Tiunov author Mari Carmen Bañuls author Aleksey K. Fedorov author MaSe department 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. American Physical Society2024 eng 0031-9007 1079-7114 2201.10220 38364163 00117927670000310.1103/PhysRevLett.132.050401 1325 Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger model. Physical Review Letters. 132(5), 050401. Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. Fractal states of the Schwinger model. <i>Physical Review Letters</i>. 2024;132(5). doi:<a href="https://doi.org/10.1103/PhysRevLett.132.050401">10.1103/PhysRevLett.132.050401</a> Petrova, Elena, Egor S. Tiunov, Mari Carmen Bañuls, and Aleksey K. Fedorov. “Fractal States of the Schwinger Model.” <i>Physical Review Letters</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/PhysRevLett.132.050401">https://doi.org/10.1103/PhysRevLett.132.050401</a>. E. Petrova, E. S. Tiunov, M. C. Bañuls, and A. K. Fedorov, “Fractal states of the Schwinger model,” <i>Physical Review Letters</i>, vol. 132, no. 5. American Physical Society, 2024. E. Petrova, E.S. Tiunov, M.C. Bañuls, A.K. Fedorov, Physical Review Letters 132 (2024). Petrova, E., Tiunov, E. S., Bañuls, M. C., &#38; Fedorov, A. K. (2024). Fractal states of the Schwinger model. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevLett.132.050401">https://doi.org/10.1103/PhysRevLett.132.050401</a> Petrova, Elena, et al. “Fractal States of the Schwinger Model.” <i>Physical Review Letters</i>, vol. 132, no. 5, 050401, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/PhysRevLett.132.050401">10.1103/PhysRevLett.132.050401</a>. 150022024-02-18T23:01:00Z2025-09-04T12:02:33Z