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

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

19 pages, 18 figures (this agrees with the published version, full form of KPZ used in the title of the revised manuscript)

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• Diagnosing quantum transport from wave function snapshots
• Critical quantum dynamics of observables at eigenstate transitions
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data