Lectures on Holographic Non-Fermi Liquids and Quantum Phase Transitions Lectures by HL at TASI 2010, Boulder, June 2010; KITPC workshop/school on 'AdS/CM duality and other approaches,' Beijing, November, 2011; School on 'Holographic View of Condensed Matter Physics' at International Institute of Physics of the Federal University of Rio Grande do Norte, Natal, Brazil, July 2011.

摘要

In these lecture notes we review some recent attempts in searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: (1) Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? (2) Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high Tc cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid," which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.