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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11336 |
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| _version_ | 1866915354206273536 |
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| author | Mallick, Arindam Andreanov, Alexei |
| author_facet | Mallick, Arindam Andreanov, Alexei |
| contents | We consider tight-binding models on Bravais lattices with anisotropic onsite potentials that vary along a given direction and are constant along the transverse one. Inspired by our previous work on flat bands in anti-\(\mathcal{PT}\) symmetric Hamiltonians [Mallick et al., Phys.~Rev.~A 105, L021305 (2022)], we construct an anti-\(\mathcal{PT}\) symmetric Hamiltonians with an \(E=0\) flat band by tuning the hoppings and the shapes of potentials. This construction is illustrated for the square lattice with bounded and unbounded potentials. Unlike flat bands in short-ranged translationally invariant Hamiltonians, we conjecture that the considered \(E=0\) flat bands do not host compact localized states. Instead the flat-band eigenstates exhibit a localization transition along the potential direction upon increasing the potential strength for bounded potentials. For unbounded potentials flat-band eigenstates are always localized irrespective of the potential strength. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flat bands in tight-binding lattices with anisotropic potentials Mallick, Arindam Andreanov, Alexei Disordered Systems and Neural Networks Quantum Gases Mathematical Physics Quantum Physics We consider tight-binding models on Bravais lattices with anisotropic onsite potentials that vary along a given direction and are constant along the transverse one. Inspired by our previous work on flat bands in anti-\(\mathcal{PT}\) symmetric Hamiltonians [Mallick et al., Phys.~Rev.~A 105, L021305 (2022)], we construct an anti-\(\mathcal{PT}\) symmetric Hamiltonians with an \(E=0\) flat band by tuning the hoppings and the shapes of potentials. This construction is illustrated for the square lattice with bounded and unbounded potentials. Unlike flat bands in short-ranged translationally invariant Hamiltonians, we conjecture that the considered \(E=0\) flat bands do not host compact localized states. Instead the flat-band eigenstates exhibit a localization transition along the potential direction upon increasing the potential strength for bounded potentials. For unbounded potentials flat-band eigenstates are always localized irrespective of the potential strength. |
| title | Flat bands in tight-binding lattices with anisotropic potentials |
| topic | Disordered Systems and Neural Networks Quantum Gases Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.11336 |