Generalized Aubry-André-Harper model with power-law quasiperiodic potentials

Abstract

We investigate a generalized Aubry-André-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i)=V{\left[\cos (2\pi \beta i)\right]}^p$. Our study reveals that the interplay between nonreciprocity, quasiperiodicity, and the power-law exponent $p$ gives rise to a variety of phase transitions and localization phenomena. In the Hermitian case, the system undergoes a direct transition from extended to localized phases for $p=1,2$, while for \(p \geq 3\), an intermediate mixed phase emerges, characterized by the coexistence of extended and localized states and the presence of mobility edges. Importantly, we find that prominent high-IPR states associated with well-resolved spectral gaps appear at specific energy levels, whose positions are captured by the relation \(x_n = nβ- \lfloor nβ\rfloor\), for low-order $n$. In the non-Hermitian regime, the energy spectrum becomes complex and the \(\mathcal{PT}\) transition coincides with the extended-to-localized phase boundary for \(p = 1, 2\), whereas for \(p \geq 3\), \(\mathcal{PT}\)-symmetry breaking occurs at the mixed-to-localized phase transition. This work reveals how power-law quasiperiodic potentials and non-reciprocal hopping govern phase transitions, providing new insight into localization phenomena of quasiperiodic systems.

16 pages, 12 figures, 2 tables

References in corpus (34)

• Anderson Transitions
• Topological Origin of Non-Hermitian Skin Effects
• Observation of parity-time symmetry breaking in a single spin system
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Many-body localization in a non-Hermitian quasi-periodic system
• Exact new mobility edges between critical and localized states
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Simulating Chern insulators on a superconducting quantum processor
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
• Dynamics of a quantum phase transition in the Aubry-André-Harper model with $p$-wave superconductivity
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Entanglement phase transitions in non-Hermitian quasicrystals
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Identifying non-Hermitian critical points with quantum metric
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Family of self-dual quasicrystals with critical Phases

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