Abstract:
Quantum matter driven away from equilibrium is a rich and fascinating physical playground. However, except in a few very special limits, many-body systems are challenging to understand. I’ll briefly discuss how we use field-theoretical techniques to develop diagrammatic Monte Carlo methods that can reliably access numerically exact dynamics in a large and important class of many-body systems: quantum impurity models. These are small interacting quantum systems coupled to a noninteracting continuum, and they can be used to model electronic dynamics and transport in mesoscopic systems coupled to an environment. They can also be used to approximately describe extended interacting quantum systems through embedding frameworks like the dynamical mean field theory (DMFT).
These tools give us unique insight into many fundamentally and technologically interesting problems. I’ll focus on two recent examples where we explored the competition between classical localization effects and quantum delocalization in the presence of many-body interactions. In one project, we applied our methods to the phase diagram of the spin–boson model—a very simple impurity model—as extracted from its transient relaxation dynamics. We showed that this reveals a transient dynamical phase diagram with different universal behavior from those of its equilibrium counterpart. In another, we proposed and solved a numerically tractable model for many-body Stark localization in the limit of large dimensions, based on an exact application of the DMFT mapping. We tracked the decay of spin-density waves, showing that as the field strengthens, transport evolves nonmonotonically from a subdiffusive regime and through a superdiffusive window, eventually becoming suppressed. This final high-field regime embodies a clear demonstration of many-body localization in the thermodynamic limit.
Our results illustrate the impact of numerically exact algorithms for simulating quantum dynamics: nonequilibrium phases are no longer speculative. Rather, they are computable, testable, and ready to be confronted with experiment.