Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

Abstract

In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-André-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents $\xi$ and $\alpha$ respectively. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized and multifractal states. We report energy-dependent transitions from ergodic to multifractal states for pairing terms with $\alpha <1$ and energy-dependent transitions from ergodic to localized states with an intermediate multifractal region for $\alpha >1$. The size of the intermediate multifractal region depends not only on the value of the superconducting pairing term $\Delta$, but also on the energy band. The transitions are not described by a mobility edge, but instead we report hybridization of bands with different types of localization properties. This leads to coexisting multifractal regimes where fractal dimensions follow different distributions.

13 pages, 10 figures

References in corpus (21)

• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Kitaev chains with long-range pairing
• Anderson localization in Bose-Einstein condensates
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Self-dual quasiperiodic systems with power-law hopping
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Localization problem of the quasiperiodic system with the spin orbit interaction
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Self-consistent theory of mobility edges in quasiperiodic chains
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Sub-diffusive phases in open clean long-range systems
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing