Flow Equation Methods for Many-Body Localization and Beyond

Flow equation methods (also known as continuous unitary transforms) are becoming a powerful new numerical tool for the analysis of a wide variety of many-body quantum systems, including disordered systems, periodically driven systems and even dissipative models. In contrast to other commonly used techniques such as tensor networks, flow equation methods are not limited by the amount of entanglement in a quantum system, and are able to efficiently simulate quantum systems in largely unexplored parameter regimes.

In this talk, I’ll outline the technique, show how it can be used to approximately diagonalize a many-body Hamiltonian (complete with rigorous error bounds) and use the method to compute local integrals of motion for disordered systems, as well as quench dynamics and correlation functions. I’ll demonstrate how the latest version of the technique can leverage the massively parallel processing power of modern graphics processing units (GPUs) to compute static and dynamic properties of not just 1D quantum systems, but 2D and even small 3D systems. A self-contained tutorial in the form of a Jupyter notebook can be found here.

Event resources