Fractal states of the Schwinger model

TL;DR

This paper investigates the fractal nature of the ground state in the lattice Schwinger model, revealing self-similarity that enables efficient prediction of ground states and energies, bridging condensed matter and high-energy physics.

Contribution

It introduces a fractal ansatz and recurrent procedure for calculating ground states in the Schwinger model, demonstrating high accuracy with few terms.

Findings

Self-similarity of the ground state in the Schwinger model.

Recurrent procedure accurately predicts ground-state energies.

Potential links between fractal properties and many-body wave function complexity.

Abstract

The lattice Schwinger model (SM), 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 the SM. 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 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.