Exact mobility edges in a slowly varying quasiperiodic ladder model

Abstract

We propose a minimal two-leg ladder model in which the mobility edge (ME) arises solely due to bond modulation, introduced through a slowly varying quasiperiodic modulation in the inter-leg tunnelling amplitudes. We demonstrate that this bond-modulated ladder naturally hosts two propagation channels, whose symmetric and antisymmetric combinations experience opposite effective onsite potentials, unlike the one-dimensional quasiperiodic models with onsite modulations. Using the adiabatic (slowly varying) limit of the modulation, we derive an exact analytical condition for the single-particle mobility edge, $E_c=\pm |2t-\lambda |,$ where $t$ is the hopping amplitude along both the legs and $\lambda$ is the bond modulation strength. This result directly generalizes the classic ME condition for slowly varying onsite potentials to a multi-leg (two-leg in our case) geometry. Extensive numerical calculations, including inverse participation ratios, Lyapunov exponents, density of states, and participation-ratio scaling, demonstrate excellent agreement with the analytical prediction across a wide range of parameters. We further identify a regime for small modulation exponents $0<\nu <1$, where localized and weakly delocalized states coexist even beyond the transition point (${\lambda }_c=2t$). Our results establish that a deterministic bond modulation can serve as a sufficient ingredient to produce an exact ME in ladder systems, offering experimentally accessible routes toward tuning nonergodic extended phases.

arXiv commentAccepted for Publication in Phy. Rev. B; Final version 16 pages, 15 figures

References in corpus (48)

• Chaos and Quantum Thermalization
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Breakdown of thermalization in finite one-dimensional systems
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Alternatives to Eigenstate Thermalization
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Anderson localization in Bose-Einstein condensates
• One-dimensional quasicrystals with power-law hopping
• Exponential localization in one-dimensional quasiperiodic optical lattices
• Observation of tunable mobility edges in generalized Aubry-André lattices
• 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
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Observation of a disordered bosonic insulator from weak to strong interactions
• 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
• Critical and bicritical properties of Harper's equation with next nearest neighbor coupling
• Exact new mobility edges between critical and localized states
• Localization transitions and mobility edges in coupled Aubry-André chains
• Topological Creutz Ladder in a Resonantly Shaken 1D Optical Lattice
• Many-body localization in incommensurate models with a mobility edge
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
• Novel mobility edges in the off-diagonal disordered tight-binding models
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• The general approach to the critical phase with coupled quasiperiodic chains
• Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Transport in the non-ergodic extended phase of interacting quasiperiodic systems
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Fate of localization in coupled free chain and disordered chain
• Probing quantum phase transition via quantum speed limit
• Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge