The structure of many-body entanglement

Abstract

In this thesis we discuss the general spatial structure of quantum entanglement in local many-body systems. A central theme is the organizing power of the renormalization group for thinking about many-body entanglement. We argue that the coarse structure of entanglement across of wide variety of systems, from gapped topological phases to gapless Fermi liquids in a variety of dimensions, can all be understood within a unified framework. We discuss tensor network states inspired by entanglement considerations, probe the limits of the boundary law for entanglement entropy, speculate about connections between entanglement renormalization and holography, and develop the formalism of mutual information in quantum field theory. We proceed from general considerations about entanglement in lattice models of many-body physics to specific attempts to isolate the low energy structure of entanglement in quantum field theories. We conclude by describing some major open questions in the subject of many-body entanglement that we find particularly interesting.