Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling

TL;DR

This paper investigates zero-energy states in a random bond square lattice model, revealing that these states are critical wave functions with multifractal properties, and introduces a non-doubling lattice fermion approach for large systems.

Contribution

It constructs a novel random lattice fermion model at zero energy without doubling and numerically demonstrates the critical, multifractal nature of zero-modes in disordered 2D systems.

Findings

Zero-modes are critical wave functions with multifractal behavior.

Large system simulations up to 801x801 confirm criticality.

The zero-mode properties align with effective field theory predictions.

Abstract

Random bond Hamiltonians of the $\pi$ flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero-modes. The states near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can construct a random lattice fermion without a doubling and quite large systems ( up to $801 \times 801$) are treated numerically. We clearly demonstrate that the zero-mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory.