Self-dual quasiperiodic systems with power-law hopping

Abstract

We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar Aubry-Andre model. For large enough $p$, their static properties are similar to those of the Aubry-Andre model, although the low-frequency conductivity in the localized phase is sensitive to $p$. For $p\le 2.1$ the Aubry-Andre localization transition splits into three transitions; two distinct intermediate regimes with both localized and delocalized states appear near the self-dual point of the Aubry-Andre model. In the intermediate regimes, the density of states is singular continuous in much of the spectrum, and is approximately self-similar: states form narrow energy bands, which are divided into yet narrower sub-bands; we find no clear sign of a mobility edge. When $p<1$, localized states are not stable in random potentials; in the present model, however, tightly localized states are present for relatively large systems. We discuss the frequency-dependence and strong sample-to-sample fluctuations of the low-frequency optical conductivity, although a suitably generalized version of Mott's law is recovered when the power-law is slowly decaying. We present evidence that many of these features persist in models that are away from self-duality.

12 pages, 20 figures; comments welcome

References in corpus (8)

• Many body localization and thermalization in quantum statistical mechanics
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• A high-accuracy algorithm for designing arbitrary holographic atom traps
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Hyperuniformity of Quasicrystals
• Differentiable potentials and metallic states in disordered one-dimensional systems

Cited by in corpus (35)

• Reentrant Localization Transition in a Quasiperiodic Chain
• Anderson localization transitions with and without random potentials
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Hidden dualities in 1D quasiperiodic lattice models
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Self-consistent theory of mobility edges in quasiperiodic chains
• Many-Body Localization with Quasiperiodic Driving
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Quantum phase transition between hyperuniform density distributions
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Quasidisorder Induced Topology
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Multifractality in the interacting disordered Tavis-Cummings model
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Critical analysis of multiple reentrant localization in an antiferromagnetic helix with transverse electric field: Hopping dimerization-free scenario
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Phase classification in the long-range Harper model using machine learning
• Subsystem localization in a two-leg ladder system
• Extended critical phase in quasiperiodic quantum Hall systems
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems
• Family of self-dual quasicrystals with critical Phases
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Universal non-power-law scaling from a chaotic renormalisation group in the Harper-Hofstadter model
• Fluctuation-stable generalized entropy probes of spectral heterogeneity