The higher Berry phase is a generalization of the Berry phase in quantum mechanics to extended quantum systems, such as quantum many-body systems on spatial lattices and quantum field theories. In this talk, I will describe how higher Berry phases can be defined and calculated for short-range entangled (invertible) quantum many-body systems using tensor networks, such as matrix product states and projected entangled pair states. I will also present a complementary formulation within the framework of quantum field theory, focusing in particular on boundary conformal field theory in 1+1 dimensions.
