A new world of topology in driven quantum systems Michael Levin 

Associate Professor
Dept. of Physics, James Franck Institute, and the College
University of Chicago 

Abstract

The first example of a so-called ``topological’’ phase of matter appeared in 1980 with Klaus von Klitzing’s discovery of integer quantum Hall liquids. Since then, many other topological phases have been discovered, including topological insulators, fractional quantum Hall liquids, and numerous other examples. Topological phases are usually studied in the context of thermal equilibrium, and there has been tremendous progress in understanding and unifying different kinds of equilibrium topological phases. However, recently it has become clear that there is a whole new world of topological phases beyond equilibrium. In particular, we now know that periodically driven systems can realize novel topological phases which have no analogs in equilibrium systems. I will discuss some recent progress in understanding and classifying these new, periodically driven topological phases of matter, as well as some of the puzzles that remain.

Research

Recently, my research has focused on two areas of quantum condensed matter physics. The first area is the study of "topological phases" of matter, such as quantum Hall liquids and topological insulators. These phases have a rich internal structure, but unlike conventional phases like magnets or superconductors, this structure has nothing to do with symmetry breaking or order parameters. Instead, the defining features of these phases have a topological character. As a result, entirely new concepts and tools need to be constructed to understand these systems. Much of my research is devoted to developing these new methods and approaches.

My second area of focus is at the intersection of quantum information theory and condensed matter physics. Here the fundamental problems are (1) to determine which quantum many-body systems can be efficiently simulated on a classical computer and (2) to develop methods to accomplish this task. In addition to its potential practical implications, this problem is closely related to many basic conceptual questions such as the nature of entanglement in many-body ground states and the classification of gapped quantum phases of matter.