I present a selective survey of the phases of quantum matter with varieties
of many-particle quantum entanglement. I classify the phases as gapped,
conformal, or compressible quantum matter. Gapped quantum matter is illustrated
by a simple discussion of the Z_2 spin liquid, and connections are made to
topological field theories. I discuss how conformal matter is realized at
quantum critical points of realistic lattice models, and make connections to a
number of experimental systems. Recent progress in our understanding of
compressible quantum phases which are not Fermi liquids is summarized. Finally,
I discuss how the strongly-coupled phases of quantum matter may be described by
gauge-gravity duality. The structure of the large N limit of SU(N) gauge
theory, coupled to adjoint fermion matter at non-zero density, suggests aspects
of gravitational duals of compressible quantum matter.Comment: 35 pages, 21 figures; Rapporteur presentation at the 25th Solvay
Conference on Physics, "The Theory of the Quantum World", Brussels, Oct 2011;
(v2+v3+v4) expanded holographic discussion and referencin
