Quantitatively assess impurity self-localization in higher-dimensional extensions

Ascertain whether the impurity self-pinning (self-localization) of an added boson at integer filling, observed in the one-dimensional all-flat-band chain of π-flux plaquettes, persists in higher-dimensional generalizations such as two-dimensional arrays of π-flux plaquettes connected by weak inter-plaquette links, and quantitatively characterize this phenomenon (e.g., existence and properties of bound states and spatial decay of the density profile) across relevant parameter regimes.

Background

The paper introduces a one-dimensional chain of π-flux plaquettes with an all-flat-band single-particle spectrum and an extensive set of local symmetries. Interactions preclude long-range chiral order via Elitzur’s theorem, and the authors identify an impurity self-pinning phenomenon: adding a single boson at integer filling yields a non-dispersive, exponentially localized density peak in the ground state.

They propose a higher-dimensional generalization (detailed in the appendix), where local symmetries also exist. While Elitzur’s theorem carries over, it remains unresolved whether the impurity self-pinning effect likewise persists in higher dimensions and, if so, how to quantify it (e.g., via bound-state formation and localization length).

References

We also point out that our model can be extended to higher dimensions; see Appendix \ref{ap:2D}. The presence of local symmetry, as well as the consequences of Elitzur theorem, are shown to directly transpose to this higher-dimensional context; the existence of the self-localization phenomenon is still to be quantitatively assessed.

— Fate of chiral order and impurity self-pinning in flat bands with local symmetry (2410.01780 - Burgher et al., 2 Oct 2024) in Conclusions (Section 6)