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Abstract
We consider the superfluid weight, speed of sound and excitation fraction of a flat band BoseEinstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing the free energy with respect to it. We find that the superfluid weight has a contribution arising from the change in the condensate density and chemical potential upon the phase twist that has been neglected in the previous literature. We also point out that the speed of sound and the excitation fraction are proportional to orbitalpositionindependent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (FubiniStudy metric) and the HilbertSchmidt quantum distance only in special cases. We derive a secondorder perturbation correction to the dependence of the speed of sound on the generalized quantum metric, and show that it compares well with numerical calculations. Our results provide a consistent connection between flat band BEC and quantum geometry, with physical observables being independent of the orbital positions for fixed hopping amplitudes, as they should, and complete formulas for the evaluation of the superfluid weight within the Bogoliubov theory. We discuss the limitations of the Bogoliubov theory in evaluating the superfluid weight.
Original language  English 

Pages (fromto)  701713 
Number of pages  13 
Journal  Low Temperature Physics 
Volume  49 
Issue number  6 
DOIs  
Publication status  Published  1 Jun 2023 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Bogoliubov theory
 flat band BoseEinstein condensate
 FubiniStudy metric
 HilbertSchmidt quantum distance
 quantum geometry.
 superfluid weight
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: Correlations in multiband quantum systems
Törmä, P. (Principal investigator), Arjas, K. (Project Member), Dahlberg, A. (Project Member), HeilmannRämö, R. (Project Member), Penttilä, R. (Project Member), Yıldırım, P. (Project Member), Taskinen, J. (Project Member), Hu, L. (Project Member), Aronen, K. (Project Member) & Pöntys, S. (Project Member)
01/09/2022 → 31/08/2026
Project: Academy of Finland: Other research funding

TEBLA: Topological Effects in Bosonic Lattices
Salerno, G. (Principal investigator)
01/06/2021 → 31/05/2023
Project: EU: MC

Longrange coherence in nanosystems
Törmä, P. (Principal investigator), Arjas, K. (Project Member), Julku, A. (Project Member), Kliuiev, P. (Project Member), Pyykkönen, V. (Project Member), Salerno, G. (Project Member), Topp, G. (Project Member), Moilanen, A. (Project Member), Kumar, P. (Project Member), Lamponen, E. (Project Member), Aronen, K. (Project Member) & Luntama, S. (Project Member)
01/01/2020 → 31/12/2021
Project: Academy of Finland: Other research funding