Fractal States of the Schwinger Model

The lattice Schwinger model, the discrete version of QED in 1 thorn 1 dimensions, is a well -studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the selfsimilarity 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.