****************  Joint CTC Condensed Matter Seminar ****************

Title:  Higher Berry structure of matrix product states

Speaker:  Prof. Ken Shiozaki (Yukawa Institute for Theoretical Physics, Kyoto University)

Date/Time: 2023-06-16 / 11:00~ 12:30

Place: P512, 5F, 3rd General Building, Nat'l Tsing Hua Univ.

Host:  Prof. Po-Yao Chang (NTHU)

Abstract:
The Berry curvature is a geometric quantity that underlies parameter-dependent quantum mechanics. Recently, the concept of a higher dimensional generalization of the Berry curvature, known as the higher Berry curvature, has been discussed [1]. In d-spatial dimensions, the higher Berry curvature is proposed as a (d+2)-form that is defined for short-range entangled states. Providing a computationally feasible method for calculating the higher Berry curvature for a given short-range entangled state is a significant challenge. In our recent work [2], we propose an explicit method to compute the higher Berry curvature for a given translationally invariant matrix product state. This method is computationally applicable for any gapped Hamiltonian. Our demonstration showed that summing up all the higher Berry fluxes across tetrahedra results in a nontrivial integer associated with the 3rd cohomology H^3(X,Z). 
[1] A. Kapustin and L. Spodyneiko, Higher-dimensional generalizations of berry curvature, Phys. Rev. B 101, 235130
(2020).
[2] Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama, Higher Berry curvature from matrix product states, arXiv:2305.08109.