Topological phases of condensed matter quantum systems

Abstract: 

Recently there has been a convergence of ideas from quantum condensed matter, quantum field theory, and quantum information theory in the study of topological phases of matter.  I will give a pedagogical overview of some of these ideas, and then describe recent progress my collaborators and I have made in understanding these phases.

Bio:

My research focus is on identifying and classifying exotic phases of matter. In particular, our group focuses on phases which cannot be understood in terms of traditional symmetry breaking Ginzburg-Landau theory, such as fractional quantum Hall phases and topological insulators (TIs). Recently we have been classifying strongly interacting versions of TIs, termed ‘symmetry protected topological’ phases, using tools such as topological quantum field theory and exactly solved models. We are also interested in other settings for realizing topological order, such as at non-zero energy density or in driven (Floquet) systems, aided by many-body localization.

Learn More:

• About Lukasz: https://phys.washington.edu/people/lukasz-fidkowski
• About his 2020 New Horizons in Physics Prize: https://breakthroughprize.org/Laureates/1/L3853 and article: https://www.washington.edu/news/2019/09/09/new-horizons-prize-fidkowski/
• See him on the CCNY Physics Colloquium (2020): https://www.youtube.com/watch?v=-2wqECJPyiE
• See him speaking on "Gravitational anomaly of 3 + 1d "Z2 toric code": https://www.youtube.com/watch?v=PwBcy2mXC1Y 

Resources:

• Introduction to topological Phases in Condensed Matter, by Adolfo G. Grushin (CNRS, 2021): https://grushingroup.cnrs.fr/wp-content/uploads/2021/06/intro_to_topo-5-1.pdf
• Three Lectures on Topological Phases of Matter, by Edward Witten (Cornell, 2016): https://arxiv.org/pdf/1510.07698
• Topological order (Wikipedia): https://en.wikipedia.org/wiki/Topological_order