Stability of flat-band Bose-Einstein condensation from the geometry of compact localized states
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915851313086464 |
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| author | Huhtinen, Kukka-Emilia |
| author_facet | Huhtinen, Kukka-Emilia |
| contents | We consider Bose-Einstein condensation in flat-band models from a real-space perspective. Using a basis of compact localized states, we reformulate the minimization of the mean-field energy as a Euclidian geometry problem. Within Bogoliubov theory, we show that flat-band models where the solutions to this problem are frameworks consisting of triangles with nonzero area are promising for condensation, whereas for instance square frameworks indicate condensation in a single mode is impossible. When restricting the analysis to Bloch states, this approach can be related to a necessary condition for a non-vanishing quantum distance. This work provides a new perspective on how condensation in flat bands is destabilized, and offers principles for the construction of models where flat-band Bose-Einstein condensation is possible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_09954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability of flat-band Bose-Einstein condensation from the geometry of compact localized states Huhtinen, Kukka-Emilia Quantum Gases We consider Bose-Einstein condensation in flat-band models from a real-space perspective. Using a basis of compact localized states, we reformulate the minimization of the mean-field energy as a Euclidian geometry problem. Within Bogoliubov theory, we show that flat-band models where the solutions to this problem are frameworks consisting of triangles with nonzero area are promising for condensation, whereas for instance square frameworks indicate condensation in a single mode is impossible. When restricting the analysis to Bloch states, this approach can be related to a necessary condition for a non-vanishing quantum distance. This work provides a new perspective on how condensation in flat bands is destabilized, and offers principles for the construction of models where flat-band Bose-Einstein condensation is possible. |
| title | Stability of flat-band Bose-Einstein condensation from the geometry of compact localized states |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2603.09954 |