Quantum seminar: Lakshya Bhardwaj (Oxford University)

 Landau Paradigm for Categorical Global Symmetries

Abstract: It is an important theoretical problem to understand phases of matter which are beyond the usual Landau paradigm based on spontaneous breaking of global symmetry groups. An idea to make progress in this direction is to enlarge our notion of global symmetries, and study the implications of their spontaneous breaking. A class of symmetry structure generalizing symmetry groups is that of symmetry (fusion) categories, whose hallmark is that they host symmetry transformations without an inverse, and are often referred to as non-invertible symmetries (or categorical symmetries).

In this talk, I will describe a general formalism, based on Symmetry Topological Field Theories (SymTFTs), for understanding the phase diagram formed by gapped and gapless phases of systems with categorical symmetries. This includes gapped and gapless symmetry protected topological (SPT) phases of matter. We will see that such phases indeed go beyond the standard Landau paradigm, e.g. spontaneous breaking of categorical symmetries can lead to physically inequivalent vacua, something which is impossible for spontaneous breaking of standard group symmetries.

References: This talk is based on works 2312.173222310.03784 and 2310.03786.

Refreshments at 10:15, followed by the talk from 10:30-12.00.