期刊
LOW TEMPERATURE PHYSICS
卷 49, 期 6, 页码 701-713出版社
AIP Publishing
DOI: 10.1063/10.0019426
关键词
flat band Bose-Einstein condensate; Bogoliubov theory; superfluid weight; Fubini-Study metric; Hilbert-Schmidt quantum distance; quantum geometry
We use multiband Bogoliubov theory to study the superfluid weight, speed of sound, and excitation fraction of a flat band Bose-Einstein condensate (BEC). The superfluid weight is determined by introducing a phase twist and minimizing the free energy. Our findings reveal that the superfluid weight includes a contribution arising from the change in condensate density and chemical potential neglected in previous studies. Furthermore, we establish a connection between the speed of sound and the excitation fraction with orbital-position-independent generalizations of quantum metric and quantum distance.
We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose-Einstein 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 orbital-position-independent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (Fubini-Study metric) and the Hilbert-Schmidt quantum distance only in special cases. We derive a second-order 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.
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