Flat Bands and Compact Localised States: A Carrollian roadmap

TL;DR

This paper demonstrates how Carrollian symmetries underpin the construction of one-dimensional fermionic systems with flat bands, highlighting the role of Compact Localised States and emergent Carroll conformal symmetry at critical points.

Contribution

It introduces a novel approach using supertranslation invariance to construct flat-band systems with inherent ultra-local correlations and emergent symmetries.

Findings

Identification of Compact Localised States via supertranslation invariance

Construction of an interacting theory with non-trivial phase structure

Emergent Carroll conformal symmetry at gapless points

Abstract

We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised States (CLSs), which appear naturally by demanding $\textit{supertranslation}$ invariance of the system. We use CLS basis states, with inherent $\textit{ultra-local}$ correlations, to write down an interacting theory which shows a non-trivial phase structure and an emergent Carroll conformal symmetry at the gapless points. We analyze this theory in detail for both zero and finite chemical potential.