Lifshitz Tails of Scale-Invariant Theories with Electric Impurities

TL;DR

This paper investigates how electric impurities affect the energy spectrum tails in scale-invariant systems, deriving asymptotic behaviors influenced by spatial dimensions and dynamical exponents.

Contribution

It provides the first analytical derivation of tail behaviors in disordered scale-invariant theories with electric impurities, highlighting the role of saddle points in disorder integrals.

Findings

Derived asymptotic expressions for density of states tails

Identified the influence of spatial dimensions and dynamical exponents

Proposed the existence of saddle points in disorder integrals

Abstract

We study scale-invariant systems in the presence of Gaussian quenched electric disorder, focusing on the tails of the energy spectra induced by disorder. For relevant disorder we derive asymptotic expressions for the densities of unit-charged states in the tails, positing the existence of saddle points in appropriate disorder integrals. The resultant scalings are dictated by spatial dimensions and dynamical exponents of the systems.