Fractal states of the Schwinger model

The Schwinger model, a discrete version of QED in two dimensions, is a well-studied test model for gauge theories on a lattice. I will tell you about the fractal properties of the Schwinger model. We have identified the self-similarity of the ground state, which allowed us to develop a recurrent procedure for finding the wave functions of the ground state and predicting the energies of the ground state. I will also tell you about the results of the recurrent calculation of ground state wave functions using a fractal ansatz and a software package for processing fractal images. In addition, I will show how the various phases present in the Schwinger model are reflected in the changing fractal structure of wave functions. Our results pave the way to understanding the complexity of calculating the many-body wave functions in terms of their fractal properties, as well as to finding new connections between models of many-particle physics and high-energy physics on lattices.