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Fractal States of the Schwinger Model
Elena V Petrova1,2, Egor S Tiunov1,3, Mari Carmen Bañuls4,5
1Russian Quantum Center, Skolkovo, Moscow 121205, Russia.
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.
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