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Equivariant Berry phase for many-body quantum lattice systems

Date and Time: Tuesday, February 22, 2022, 02:30pm -

Speaker: Anton Kapustin (Caltech)


Berry phase as originally defined makes sense only for quantum systems with a finite-dimensional Hilbert space. However, it does have important generalizations to many-body systems. In this talk I will describe some generalizations of the Berry phase to the case of quantum lattice systems in infinite volume. The Hall conductance and its nonabelian versions emerge as special cases. The results can be viewed as a generalizations of the von Neumann - Wigner theorem on level crossing in quantum systems.

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