# The Quantum Phases of Matter

 Title: The Quantum Phases of Matter Author: Sachdev, Subir Citation: Sachdev, 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. Full Text & Related Files: Sachdev_ Quantum.pdf (2.491Mb; PDF) Abstract: 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 $$Nc \rightarrow \infty$$ 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. Other Sources: http://arxiv.org/abs/1203.4565 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10885508 Downloads of this work: