Quantum Critical Systems from AdS/CFT

Abstract

The AdS/CFT (anti-de Sitter/conformal field theory) correspondence enables us to construct some strongly coupled quantum field theories by means of general relativity, and this approach provides new universality classes of condensed matter systems. In this dissertation, we will consider three systems.

The first system (chapter 2) is the Reissner-Nordstrom (RN)-AdS_4 black hole at finite temperature. By solving the Dirac equation for a massive, charged spinor in this background, we find that the fermions have a Rashba-like dispersion relation, and the Fermi surface has a spin-orbit helical locking structure. We use an improved WKB method that takes into account the spin-orbit coupling. The effective potential has a potential well with a barrier. The quasibound states in the potential well can tunnel through the barrier into the horizon, giving an imaginary part to the mode.

The second system (chapter 3) is the two-charge black hole in AdS_5 at zero temperature, which gives an analytically solvable model for the holographic Fermi surface. Descending from type IIB supergravity, the two-charge black hole describes N coincident D3-branes with equal, nonzero angular momenta in two of the three independent planes of rotation orthogonal to the D3-brane world volume. The IR geometry of the extremal two-charge black hole is conformal to AdS_2xR^3, and the electric field vanishes in the near horizon limit.

The third system (chapter 4) is the extremal RN-AdS_5 black hole, in which quantum criticality is studied by solving the Klein-Gordon equation. The Green's function near quantum critical points is analytically obtained. There are two types of instability: the first one is triggered by a zero mode, and gives a hybridized critical point; the second one is triggered by the instability of the IR geometry, and gives a bifurcating critical point.