Quantum criticality in the disordered Aubry-André model

Abstract

In this paper, we explore quantum criticality in the disordered Aubry-André (AA) model. For the pure AA model, it is well-known that it hosts a critical point separating an extended phase and a localized insulator phase by tuning the strength of the quasiperiodic potential. Here we unearth that the disorder strength $\Delta$ contributes an independent relevant direction near the critical point of the AA model. Our scaling analyses show that the localization length $\xi$ scales with $\Delta$ as $\xi \propto {\Delta }^{-{\nu }_{\Delta }}$ with ${\nu }_{\Delta }$ a new critical exponent, which is estimated to be ${\nu }_{\Delta }\approx 0.46$. This value is remarkably different from the counterparts for both the pure AA model and the Anderson model. Moreover, rich critical phenomena are discovered in the critical region spanned by the quasiperiodic and the disordered potentials. In particular, in the extended phase side, we show that the scaling theory satisfy a hybrid scaling form as a result of the overlap between the critical regions of the AA model and the Anderson localization.

7 pages, 7 figures

References in corpus (17)

• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization of ultrasound in a three-dimensional elastic network
• Quantum criticality
• Topological phase transition in non-Hermitian quasicrystals
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Many-body localization in a non-Hermitian quasi-periodic system
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes

Cited by in corpus (14)

• Localization Driven Quantum Sensing
• Quantum criticality and Kibble-Zurek scaling in the Aubry-André-Stark model
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Kibble-Zurek scaling in one-dimensional localization transitions
• Stark localization near Aubry-André criticality
• Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Phase transitions in non-Hermitian superlattices
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Localization with non-Hermitian off-diagonal disorder
• Critical spin models from holographic disorder