2020 McMillan Award Lecture - "Many-body physics in the NISQ era"

A central goal of condensed matter physics is to study the universal emergent properties of macroscopic quantum systems with large numbers of interacting particles. Due to a variety of conceptual and experimentally motivated reasons, the traditional approach of many-body physics is largely built around the study of low-temperature and near-equilibrium properties of time independent Hamiltonians.  

 A confluence of developments across a range of subfields --- particularly experimental advances in building Noisy Intermediate-Scale Quantum (NISQ) devices --- have opened up a vast new territory of studying many-body phenomena in completely novel regimes: highly excited, "post Hamiltonian", and far from equilibrium. The natural evolutions implemented by these novel experiments are dynamics generated by quantum circuits of unitary gates, possibly interrupted by measurements, and starting from initial states that are not low energy in any useful sense. 

 I will describe some highlights of an active research program to advance many-body theory beyond the regime of near-equilibrium time-independent Hamiltonians, with a view towards uncovering novel emergent phenomena in the non-equilibrium dynamics of many-body systems and the physics of quantum circuits. A notable recent example is the discovery of the time-crystal, a phase of matter that is provably disallowed in thermal equilibrium, but has a sharp dynamical realization in an out-of-equilibrium setting. I will also discuss other universal features of quantum dynamics that have been obtained by studying different classes of unitary and non-unitary quantum circuits, including a recent discovery of steady state dynamical phases with fractal entanglement scaling.