Exact New Mobility Edges between Critical and Localized States.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Disordered Systems

Background:

• Disordered quantum systems exhibit extended, localized, and critical states.
• Critical states in these systems are significantly less explored.
• Mobility edges (MEs) delineate transitions between different quantum state types.

Purpose of the Study:

• To propose a new class of exactly solvable models for disordered systems.
• To identify novel mobility edges (MEs) separating localized and robust critical states.
• To propose a feasible experimental realization of these models and MEs.

Main Methods:

• Development of exactly solvable one-dimensional models with quasiperiodic potentials and hopping terms.
• Analytical derivation of critical states and mobility edges.
• Proposal of an experimental scheme using an incommensurate Rydberg Raman superarray.

Main Results:

• Discovery of a novel type of exact mobility edge (ME) separating localized from robust critical states.
• Demonstration of the robustness of critical states against single-particle perturbations and few-body interactions.
• Identification of zeros in quasiperiodic hopping terms as a protective mechanism for critical states.

Conclusions:

• The proposed exactly solvable models provide an unambiguous route to study critical states and novel MEs.
• The identified mechanism offers a generic pathway for protecting critical states in disordered systems.
• The experimental proposal enables feasible exploration of critical state physics and new ME phenomena.