Existence of non-ergodic many-body states in dimensions greater than one

Determine whether non-ergodic states exist in many-body systems in more than one spatial dimension (D > 1).

Background

The paper investigates disorder-driven breakdown of ergodicity in a two-dimensional array of superconducting qubits, focusing on signatures of a non-ergodic extended (NEE) regime distinct from fully ergodic and fully localized (MBL) phases. While NEE phases are supported in various infinite-range and random matrix models, their realization in realistic finite-dimensional systems is actively debated.

The authors note that although several works argue against the stability of MBL phases in higher dimensions, these arguments do not exclude non-ergodic behavior such as NEE. Numerical studies are challenging due to the exponential Hilbert-space volume, leaving unresolved whether genuinely non-ergodic states exist beyond one spatial dimension.