Quantum Encounters Seminar -- Quantum Information, Condensed Matter, Quantum Field Theory

Noncommutative Geometry of Quantum Lattice Models and the Higher Berry Phase

by Anton Kapustin (Caltech)

Zoom Réunion

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.


ID de réunion : 817 7896 2715
Code secret : 800452

Organized by

Vasily Pestun & Slava Rychkov