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Flat Bands and Compact Localised States: A Carrollian roadmap
by Nisa Ara, Aritra Banerjee, Rudranil Basu, Bhagya Krishnan
Submission summary
| Authors (as registered SciPost users): | Aritra Banerjee |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2412.18965v2 (pdf) |
| Date submitted: | 2025-01-14 15:20 |
| Submitted by: | Banerjee, Aritra |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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 supertranslation invariance of the system. We use CLS basis states, with inherent 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
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Report
In this work, the authors studied how to use the Carrollian symmetry to construct one-dimensional lattice fermionic systems with all flat-band spectra. They discovered a striking relation between the compact localized states (CLS) and Carrollian symmetry. They showed that the CLS modes, which are essential in generating flat-band system, can be generated by the supertranslation transformation in Carrollian quantum field theory. With the site-local CLS modes, they were allowed to construct the supertranslation invariant interaction terms. In the work, they introduced four-fermion interactions into the systems and studied the quantum phase structure, both with the filling factor constrained at half and unconstrained.
The work presents some novel and important findings. It may lead to further studies of the strongly correlated systems with emergent ultra-local features from Carrollian symmetry point of view. I would like to recommend it for publication in its present form.
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