Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model

TL;DR

This paper explores the dynamical universality classes of a driven one-dimensional quasiperiodic quantum model, revealing Family-Vicsek scaling, critical phase fragility, and KPZ-like superdiffusive growth in surface roughness.

Contribution

It introduces the Family-Vicsek scaling in quantum surface-roughness and uncovers KPZ-like superdiffusive behavior in a driven quasiperiodic system, a novel quantum dynamical phenomenon.

Findings

Family-Vicsek scaling observed in quantum surface-roughness.

Critical phase is fragile under periodic driving.

Driven system exhibits KPZ-like superdiffusive growth.

Abstract

The investigation of the dynamical universality classes of quantum systems is an important, and rather less explored, aspect of non-equilibrium physics. In this work, considering the out-of-equilibrium dynamics of spinless fermions in a one-dimensional quasiperiodic model with and without a periodic driving, we report the existence of the dynamical one-parameter based Family-Vicsek (FV) scaling of the "quantum surface-roughness" associated with the particle-number fluctuations. In absence of periodic driving, the model is interestingly shown to host a subdiffusive critical phase separated by two subdiffusive critical lines and a triple point from other phases. An analysis of the fate of critical phase in the presence of (inter-phase) driving indicates that the critical phase is quite fragile and has a tendency to get absorbed into the delocalized or localized regime depending on the driving parameters. Furthermore, periodic driving can conspire to show quantum Kardar-Parisi-Zhang (KPZ)-like superdiffusive dynamical behavior, which seems to have no classical counterpart. We further construct an effective Floquet Hamiltonian, which qualitatively captures this feature occurring in the driven model