Logarithmic Operators and Hidden Continuous Symmetry in Critical Disordered Models

TL;DR

This paper analyzes a (2+1)-dimensional relativistic fermion model at criticality with random gauge potential, revealing a hidden continuous symmetry and logarithmic behavior in correlation functions, with implications for local density of states distribution.

Contribution

It uncovers a hidden continuous symmetry and logarithmic operators in a critical disordered fermion model, providing exact solutions and new insights into its operator structure.

Findings

Presence of a conserved current generating continuous symmetry

Logarithmic contributions to correlation functions at criticality

Local density of states follows a log-normal distribution

Abstract

We study the model of (2 + 1)-dimensional relativistic fermions in a random non-Abelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current - a generator of a continuous symmetry. The presence of this operator changes the operator product expansion and gives rise to logarithmic contributions to the correlation functions at the critical point. We calculate the distribution function of the local density of states in this model and find that it follows the famous log-normal law.