Sachdev, Subir2013-07-252012Sachdev, Subir. 2012. The quantum phases of matter. In The Theory of the Quantum World Proceedings of the 25th Solvay Conference on Physics: 19-22 October, 2011, Santa Barbara, CA, ed. David Gross, Marc Henneaux, and Alexander Sevrin. Singapore: World Scientific Publishing.9789814518840http://nrs.harvard.edu/urn-3:HUL.InstRepos:10885508I 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 \(Nc \rightarrow \infty\) limit of \(SU(N_c)\) gauge theory, coupled to adjoint fermion matter at non-zero density, suggests aspects of gravitational duals of compressible quantum matter.en-UShigh energy physicsquantum physicsConference Paper2013-07-25