Flat Bands and Compact Localised States: A Carrollian roadmap
arXiv:2412.18965 · doi:10.21468/SciPostPhys.19.2.046
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 invariance of the system. We use CLS basis states, with inherent 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.
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