Fermions and the AdS/CFT correspondence: quantum phase transitions and the emergent Fermi-liquid

A central mystery in quantum condensed matter physics is the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. Field theoretical statistical techniques are useless because of the fermion sign problem, but we will present here results showing that the mathematics of string theory is capable of describing fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theory. Deforming away from the relativistic quantum critical point by increasing the fermion density we show that a state emerges with all the features of the Fermi-liquid. Tuning the scaling dimensions of the critical fermion fields we find that the quasiparticle disappears at a quantum phase transition of a purely statistical nature, not involving any symmetry change. These results are obtained by computing the solutions of a classical Dirac equation in an AdS space time containing a Reissner-Nordstrom black hole, where the information regarding Fermi-Dirac statistics in the field theory is processed by quasi-normal Dirac modes at the outer horizon.