Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants

Abstract

We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of quasiperiodic systems are characterized by RG fixed points associated with renormalized single-band models. We identify fixed-points that include many previously reported exactly solvable quasiperiodic models. By classifying relevant and irrelevant perturbations, we show that phase boundaries of more generic models can be determined with exponential accuracy in the approximant's unit cell size, and in some cases analytically. Our findings provide a unified understanding of widely different classes of 1D quasiperiodic systems.

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• Topological inverse Anderson insulator
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• A numerical study of the localization transition of Aubry-André type models
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• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
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• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
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• Experimental observation of exact quantum critical states
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Quasiperiodic Quadrupole Insulators
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Detecting the $\pi$-axiverse through parametric resonance
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Fractal Quasicondensation in One Dimension
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices