Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge

Abstract

We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-André-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the imbalance, we get hints of a rich phase diagram. We find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current. Current is calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a 'critical' line separating regions of ballistic and localized transport. Like critical point of AAH model, current scales sub-diffusively with system size on the 'critical' line ($I\sim N^{-2\pm 0.1}$). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where $I\sim N^{-1.4\pm 0.05}$). All these results can be understood from the above-mentioned connection between states near mobility edge of GAAH model and those of critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.

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• Anderson Transitions
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Roton-type mode softening in a quantum gas with cavity-mediated long-range interactions
• Signatures of Many-Body Localization in a Controlled Open Quantum System
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Cited by in corpus (6)

• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Dephasing enhanced transport in boundary-driven quasiperiodic chains
• Fluctuation-stable generalized entropy probes of spectral heterogeneity