Quantum diffusion in two-dimensional random systems with particle-hole symmetry

TL;DR

This paper investigates how particle-hole symmetry induces diffusion in two-dimensional random systems, revealing a unique form of asymptotic freedom described by Grassmann fields.

Contribution

It demonstrates that particle-hole symmetry leads to diffusion in 2D random systems and introduces a Grassmann field description indicating asymptotic freedom.

Findings

Diffusion occurs in 2D systems with particle-hole symmetry.

Diffusion is described by a non-interacting Grassmann field.

A form of asymptotic freedom is identified in the model.

Abstract

We study the scattering dynamics of an $n$-component spinor wavefunction in a random environment on a two-dimensional lattice. In the presence of particle-hole symmetry we find diffusion on large scales. The latter is described by a non-interacting Grassmann field, indicating a special kind of asymptotic freedom in $d=2$.