We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.

中文翻译：

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量子几何与平带玻色-爱因斯坦凝聚

我们通过使用多带 Bogoliubov 理论研究了平带晶格系统中弱相互作用的玻色-爱因斯坦凝聚 (BEC) 的性质，并发现了与基础量子几何的基本联系。在平坦带中，声速和凝聚态的量子损耗由量子几何决定，凝聚态和其他态之间的有限量子距离保证了 BEC 的稳定性。我们的结果表明，即使在相互作用较弱的情况下，合适的量子几何也可以达到强量子相关性。