Emergent quantum criticality, Fermi surfaces, andAdS2

Abstract

Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region which is AdS2 × R d−1 . The scale invariance of the AdS2 region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a (0+1)-dimensional CFT. This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the "Marginal Fermi Liquid" form, postulated to describe the optimally doped cuprates.

Holographic antiferromagnetic quantum criticality andAdS2scaling limit

“…As the similar situation in Ref. [33], we will see that our numerical results about the behaviors in the vicinity of QCP are just controlled by the IR geometry which is just the emergent AdS 2 geometry.…”

“…In order to analytically study the critical behavior in the vicinity of QCP, we employed the IR-UV matching method in Ref. [33], and the results show that the analytical method confirms the numerical results obtained in Ref. [28].…”

“…Then using the method in Ref. [33], one can find that the retarded Green's function can be expanded in small ω as (40), the retarded Green's function can be written as the following form for small ω and q,…”

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

“…The conventional boundary term to be chosen is the Lorentz covariant one, i.e., 8) whereby the variation of the full on-shell action reads 9) which apparently vanishes if the Dirichlet boundary condition is imposed on ψ + . This choice of boundary condition is usually referred to as the standard quantization for the Dirac field.…”

“…Speaking specifically, with the fermionic correlator, which can be extracted at the boundary holographically by evolving the bulk Dirac equation in the Reissner-Nordstrom AdS black hole with the ingoing boundary condition at the horizon, one can read off the Fermi surface with a rich spectrum of non-Fermi liquid behaviors [6,7,8,9,10,11,12,13]. However, as is well known, the Reissner-Nordstrom AdS black hole has a large ground state degeneracy, namely a finite entropy at zero temperature, which is somehow in tension with the third law of thermodynamics.…”