Local quantum critical point and non-Fermi liquid properties

Quantum criticality provides a means to understand the apparent non-Fermi liquid phenomena in correlated electron systems. How to properly describe quantum critical points in electronic systems has however been poorly understood. The issues have become particularly well-defined due to recent experiments in heavy fermion metals, in which quantum critical points have been explicitly identified. In this paper, I summarize some recent theoretical work on the subject, with an emphasis on the notion of ``local quantum criticality''. I describe the microscopic work based on an extended dynamical mean field theory, as well as Ginzburg-Landau arguments for the robustness of the local quantum critical point beyond the microscopics. I also present the consequences of this picture on the inelastic neutron scattering, NMR, Fermi surface properties and Hall coefficient, and compare them with the available experiments. Some analogies with the Mott transition phenomena are also noted.