Abstract: Over the last several decades, entanglement has emerged as a unifying lens for understanding phenomena across many areas in quantum physics. At low energy, the structure of ground state entanglement reflects universal features of the phase of matter. At high energy, the growth of entanglement underlies thermalization and the emergence of statistical mechanics. In this talk, I will describe two recent exact results characterizing entanglement in many-body systems.
First, we will consider the entanglement entropy in momentum space of translation-invariant Fermi liquids and superconductors. By developing a non-perturbative expansion in the k-space volume of the partition, we will discover a universal function of low energy parameters hiding in the entropy.
Second, we will consider how Hilbert space constraints, arising from symmetry or local rules, change the typical entanglement of random pure states. By an exact diagrammatic approach, I will compute entanglement spectra. The singularities in these spectra naturally organize constraints and symmetries into "phases".
Location: ATL 4402