290S/290K Quantum Materials Seminar: Niclas Heinsdorf (Max Planck Institute for Solid State Research); Wednesday, April 17 at 2:00 PM Pacific Time in 402 Physics South
Time/Venue: Wednesday, April 17 at 2:00 PM Pacific Time in 402 Physics South and via Zoom:
https://berkeley.zoom.us/j/99523499113?pwd=REovb3pyam03WXQwbEhrU3dqNHZvdz09
Meeting ID: 995 2349 9113 Passcode: 600704
Host: Ehud Altman, Bartholomew Andrews
Title: Higher Berry Curvature in Interacting Fermion Systems
Abstract: The higher Berry curvature was introduced by Kapustin and Spodyneiko as an extension of the Berry curvature in quantum mechanical systems with finite degrees of freedom to quantum many-body systems in finite spatial dimensions. In this talk, I showcase an alternative formulation of the higher Berry curvature using translationally invariant matrix product states. They are the ground states of a set of gapped Hamiltonians which are evolved adiabatically through a discretized parameter space, and moreover represent interacting many-body wave functions. Because matrix product states transform under a projective representation, evaluating the Berry curvature on a closed loop through parameter space is not sufficient to fix all the gauge degrees of freedom. To obtain a gauge-invariant real quantity, the higher-dimensional Berry curvature is evaluated on small tetrahedra in parameter space. Numerical calculations confirm that the higher Berry curvature varies continuously throughout an adiabatic evolution and becomes quantized over a closed 3-dimensional parameter space. I demonstrate that the procedure works for fermions too, showing the correspondence of the higher invariant and the second Chern number for the free-fermion four-dimensional topological insulator. Lastly, I add many-body interactions, which have a nontrivial effect on the higher Berry curvature, and can lead to topological phase transitions.
See the Physics Department Calendar for future seminars.