Lattice-induced wave-function effects on trapped superfluids

Wave-function effects in uncorrelated systems are characterized by the Berry curvature and quantum metric. Beyond those, we propose gauge-independent tensors describing Bloch wave-function effects on local interaction between correlated particles. We derive an effective hydrodynamic theory for ultracold bosons in optical lattices. Ground states and collective modes of superfluids in isotropic harmonic traps are solved for highly symmetric lattices. In a dynamic process, the wave-function effects are featured by the eigenfrequency, amplitude, and phase shift of an excited breathing mode and can be observed in experiments. We also give a tight-binding model of a bipartite square lattice with nontrivial wave-function effects, where results are estimated with typical experimental parameters. Our discovery advances the connections between the modern band theory and quantum many-body physics.