Fractal states of the Schwinger model

• URL: http://arxiv.org/abs/2201.10220v1
• Date: Tue, 25 Jan 2022 10:20:45 GMT
• Title: Fractal states of the Schwinger model
• Authors: E.V. Petrova, E.S. Tiunov, M.C. Ba\~nuls, A.K. Fedorov
• Abstract summary: The lattice Schwinger model is a well-studied test bench for lattice gauge theories. We reveal the self-similarity of the ground state, which allows one to develop a recurrent procedure for finding the ground-state wave functions. Our findings pave the way to understand the complexity of calculating many-body wave functions in terms of their fractal properties.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 fractal properties of the Schwinger model. We reveal the self-similarity of the ground state, which allows one to develop a recurrent procedure for finding the ground-state wave functions and predicting ground state energies. We provide the results of recurrently calculating ground-state wave functions using fractal ansatz and automized software package for fractal image processing. In some 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. In addition, we show how the different phases present in the Schwinger model are reflected in a changing fractal structure of the wave functions. Our findings pave the way to understand the complexity of calculating many-body wave functions in terms of their fractal properties as well as to find new links between condensed matter and high-energy lattice models.

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