Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models

TL;DR

This study reveals dynamical one-parameter scaling in disordered fermion models, linking surface roughness and entanglement entropy, with unique quantum effects leading to anomalous scaling exponents.

Contribution

It introduces the concept of dynamical scaling in quantum disordered systems and uncovers disorder-dependent exponents, including anomalous scaling in the random-dimer model.

Findings

Dynamical scaling observed for surface roughness and entanglement entropy.

Scaling exponents depend on disorder type.

Partially localized states cause anomalous scaling effects.

Abstract

Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically study dynamics of fermions on disordered onedimensional potentials exhibiting localization and find dynamical one-parameter scaling for surface roughness, which represents particle-number fluctuations at a given lengthscale, and for entanglement entropy when the system is in delocalized phases. This dynamical scaling corresponds to the Family-Vicsek scaling originally developed in classical surface growth, and the associated scaling exponents depend on the type of disorder. Notably, we find that partially localized states in the delocalized phase of the random-dimer model lead to anomalous scaling, where destructive interference unique to quantum systems leads to exponents unknown for classical systems and clean systems.