Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

Abstract

The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied in three dimensional disorder systems and one-dimensional quasiperiodic systems. However, the studies of MEs in two dimensional (2D) systems are rare. Here we propose a class of 2D vertex-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of a (extended) Lieb lattice. By mapping these models to the 2D Aubry-André model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials. Finally, we propose a highly feasible scheme to experimentally realize our model in a quantum dot array. Our results open the door to studying and realizing exact MEs and robust flat bands in 2D systems.

References in corpus (29)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Universal control of a six-qubit quantum processor in silicon
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• A four-qubit germanium quantum processor
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Quantum error correction with silicon spin qubits
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Flat Bands Under Correlated Perturbations
• Anderson localisation in tight-binding models with flat bands
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Loading a quantum-dot based "Qubyte" register
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Anderson localization transitions with and without random potentials
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Quantum phase with coexisting localized, extended, and critical zones
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Flat-band-based multifractality in the all-band-flat diamond chain
• Coexistence of localization and transport in many-body two-dimensional Aubry-André models
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Localization and criticality in antiblockaded 2D Rydberg atom arrays

Cited by in corpus (9)

• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Dissipation-Driven Transition of Particles from Dispersive to Flat Bands
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping