Abstract: The patterns of self-organization in complex quantum systems are traditionally
understood using the concept of spontaneous symmetry breaking. In contrast,
quantum order in the absence of symmetry breaking, in particular highly
entangled topologically ordered states, describe fundamentally distinct phases
of matter which are of great interest both in present-day condensed matter
research and in quantum information science. In this talk, I will spend some
time reviewing the concepts of topological and non-symmetry broken quantum
order. I will then focus on the interplay of such exotic states with gapless
fermions, i.e., metals. I will discuss their importance as solid-state
realizations of lattice gauge theories, mechanisms in which a Fermi sea
stabilizes miniature variants of topological order, and experimental setups in
which metallic contacts are used to probe quantum order. I will conclude with
an outlook summarizing the multiple synergies of quantum information theory and
quantum materials science.