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arXiv:1912.04529 · Journal of Superconductivity and Novel Magnetism

Explanation of Superfluidity Using the Berry Connection for Many-Body Wave Functions

Hiroyasu Koizumi

Published Feb 19, 2020• 17 citations
arXivHTMLPDF
DOI
10.1007/s10948-020-05438-w

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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.
In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase---a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wave-function overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized matrix product states (MPS) over a parameter space. We demonstrate the use of our formula for simple nontrivial models.