Exact mobility edges in quasiperiodic network models with slowly varying potentials

Abstract

Quasiperiodic models are important physical platforms to explore Anderson transitions in low dimensional systems, yet the exact mobility edges (MEs) are generally hard to be determined analytically. To date, the MEs in only a few models can be determined exactly. In this manuscript, we propose a new class of network models characterized by quasiperiodic slowly varying potentials and the absence of hidden self-duality, and exactly determine their MEs. We take the mosaic models with slowly varying potentials as examples to illustrate this result and derive its MEs from the effective Hamiltonian. In this method, we can integrate out the periodic sites to obtain an effective Hamiltonian with energy-dependent potentials $g(E)V$ and effective eigenenergy $f(E)$, which directly yields the MEs at $f(E)=\pm (2t^{\kappa }\pm g(E)V)$, where $\kappa \in {\mathbb{Z}}^{+}$. With this idea in hand, we then generalize our method to more quasiperiodic network models, including those with much more complicated geometries and non-Hermitian features. Finally, we propose the realization of these models using optical waveguides and show that the Anderson transition can be observed even in small physical systems (with lattice sites about $L=50-100$). Our results provide some key insights into the understanding and realization of exact MEs in experiments.

13 pages, 10 figures

References in corpus (57)

• Quantum Simulation
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Atomic physics and quantum optics using superconducting circuits
• Topological States and Adiabatic Pumping in Quasicrystals
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Simulators: Architectures and Opportunities
• Probing entanglement in a many-body-localized system
• Localization and delocalization of light in photonic moire lattices
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Tools for quantum simulation with ultracold atoms in optical lattices
• Topological phase transition in non-Hermitian quasicrystals
• Fast Scalable State Measurement with Superconducting Qubits
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Theory of the many-body localization transition in one dimensional systems
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Measurement of the mobility edge for 3D Anderson localization
• Many-body localization characterized from a one-particle perspective
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Experimental Two-dimensional Quantum Walk on a Photonic Chip
• Measurement and Control of Quasiparticle Dynamics in a Superconducting Qubit
• One-dimensional quasicrystals with power-law hopping
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Reentrant Localization Transition in a Quasiperiodic Chain
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Many body localization in the presence of a single particle mobility edge
• Demonstration of a Tuneable Coupler for Superconducting Qubits Using Coherent, Time Domain, Two-Qubit Operations
• Digital Quantum Simulation of Spin Systems in Superconducting Circuits
• Interface Between Topological and Superconducting Qubits
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Exact new mobility edges between critical and localized states
• Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model
• Anderson localization of electromagnetic waves in three dimensions
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Two-dimensional Thouless pumping of light in photonic moiré lattices
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Universality in Anderson localization on random graphs with varying connectivity
• Scalable cold-atom quantum simulator for two-dimensional QED
• Novel mobility edges in the off-diagonal disordered tight-binding models
• The general approach to the critical phase with coupled quasiperiodic chains
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Fate of localization in coupled free chain and disordered chain