Matrix product state and higher Berry curvature

by Dr Ken Shiozaki (Yukawa Institute)

Tuesday 25 Jun 2024, 11:00 → 12:00 Europe/Zurich

WHGA/121

The Berry curvature is a geometric quantity that underlies parameter-dependent quantum me-
chanics. Recently, the concept of a higher dimensional generalization of the Berry curvature,
known as the higher Berry curvature, has been proposed [1]. In d-spatial dimensions, the higher
Berry curvature is proposed as a (d + 2)-form that is de ned for short-range entangled states.
Providing a computationally feasible method for calculating the higher Berry curvature for a
given short-range entangled state is challenging. We propose an explicit method to compute
the higher Berry curvature for a given translationally invariant matrix product state for a 1-
dimensional short-range entangled state [2]. Our demonstration showed that summing up all
the higher Berry  uxes across tetrahedra results in a nontrivial integer associated with the 3rd
cohomology H3(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, and Shuhei Ohyama, Higher Berry curvature from matrix
product states, arXiv:2305.08109