Noncommutative Geometry of Quantum Lattice Models and the Higher Berry Phase

by Anton Kapustin (Caltech)

Tuesday Apr 27, 2021, 5:00 PM → 6:00 PM Europe/Paris

Zoom Réunion

Recently methods of quantum statistical mechanics have been fruitfully applied to the study of phases of quantum lattice systems at zero temperature. For example, a rigorous definition of a Short-Range Entangled phase of matter has been given and a classification of such phases in one spatial dimension has been achieved. I will discuss some of these developments, focusing on the topology and geometry of the space of Short-Range Entangled states. According to a conjecture of A. Kitaev, these spaces form a loop spectrum in the sense of homotopy theory. This conjecture implies that to any family of Short-Range entangled states in one dimension one can associate a gerbe on the parameter space. I will show how to construct such a gerbe. Thе curvature of this gerbe is a closed 3-form with quantized periods and can be regarded as a higher-dimensional generalization of the curvature of the Berry connection.

https://us02web.zoom.us/j/81778962715?pwd=QnpNS2ErSnBCTWRYUHphd1VMMysyZz09

ID de réunion : 817 7896 2715
Code secret : 800452