From the three-body problem to the butterfly effect, chaos is one of the most mathematically fascinating yet tangible phenomena in nature. Chaos in the classical world has been (more or less) well understood and formulated in the language of dynamical systems, but its quantum counterpart remains elusive — even its definition is not clear despite decades of efforts. We will discuss a new way to look at the problem: instead of focusing on quantum states, we aim to uncover the chaotic behavior of a many-body quantum system by studying the entanglement of operators. We will test this idea in the context of conformal field theories, which describe critical phenomena in condensed matter systems and are tightly related to quantum gravity in high energy physics. In particular, we show that nature may have a bound on chaos, and illustrate certain critical systems, which are closely connected to black hole physics, that saturate this universal bound.
Dr. Nie is a condensed matter theorist, with a 2017 PhD, presently a Kadanoff Postdoctoral Fellow at the University of Chicago. She works on novel superconductors, quantum chaos, and quantum information science.