Exact new mobility edges between critical and localized states

TL;DR

This paper introduces exactly solvable models with novel mobility edges separating localized and critical states, providing analytical insights and proposing experimental realization in Rydberg superarrays.

Contribution

It presents a new class of exactly solvable models with robust mobility edges between localized and critical states, advancing understanding of critical quantum states.

Findings

Exact analytical solutions for mobility edges

Critical states protected by zeros of quasiperiodic hopping

Proposed experimental realization in Rydberg superarrays

Abstract

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This work may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.