Higher Berry curvature and group action on parameter space in spin chain systems

Ken Shiozaki^1*

¹Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan

* Presenter:Ken Shiozaki, email:ken.shiozaki@yukawa.kyoto-u.ac.jp

Recently, the global structure of invertible quantum many-body states has been elucidated. A pure state is called invertible if it can be realized as the unique gapped ground state of a Hamiltonian with local terms. In particular, one-dimensional invertible states carry a three-form higher Berry curvature in the parameter space, which generalizes the conventional two-form Berry curvature in quantum mechanical systems.
In this talk, I will present how group actions on both the parameter space and the Hilbert space give constraints on the global structure of invertible states, using the matrix product state representation. As an application of this formalism, we show that the phase transition point between the Haldane chain phase and the trivial phase behaves as a source of the three-form higher Berry curvature.
Ref: KS arXiv:2507.19932.

Keywords: matrix product state, higher Berry curvature, parameter family , spin chains, topological phases