# Quantum lattice Boltzmann study of random-mass Dirac fermions in one dimension

## TL;DR

This paper uses quantum lattice Boltzmann simulations to investigate how random mass disorder affects the time evolution of Dirac fermions in one dimension, revealing algebraic localization behavior.

## Contribution

It introduces a novel simulation approach to study disordered Dirac fermions and uncovers algebraic decay in localization, contrasting with typical exponential Anderson localization.

## Key findings

- Diffusion halts after finite time with nonzero disorder
- Disorder-averaged density exhibits algebraic decay ~ x^{-3/2}
- Results align with analytic predictions for zero-energy solutions

## Abstract

We study the time evolution of quenched random-mass Dirac fermions in one dimension by quantum lattice Boltzmann simulations. For nonzero noise strength, the diffusion of an initial wave packet stops after a finite time interval, reminiscent of Anderson localization. However, instead of exponential localization we find algebraically decaying tails in the disorder-averaged density distribution. These qualitatively match $\propto x^{-3/2}$ decay, which has been predicted by analytic calculations based on zero-energy solutions of the Dirac equation.