Effective holographic theories for low-temperature condensed matter systems

Abstract

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents (γ, δ) that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the (γ, δ) plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when γ = δ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole (γ, δ) plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

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

“…First, besides going beyond the massless case and heating up the dual soup to the finite temperature, it is interesting to investigate the probe fermion in other desirable dilatonic black holes such as those obtained in [22,23], where the near horizon geometry has a favorable Lifshitz symmetry. In addition, as done in [24,25,26,27,28], one is also tempted to investigate how the fermionic correlator is modified in the presence of the bulk dipole coupling.…”

Transport properties of spacetime-filling branes

“…In these cases the model is studied and improved without worrying much about string theory embeddings, but about the physical consequences extracted from it. An example is the study of theories with Lifshitz scaling and hyperscaling violation from a theory of Einstein gravity coupled to a dilatonic scalar and a U(1) gauge field [13,14], which allows to study theories with broken Lorentz symmetry under a better control than the top-down models, or the 'Improved Holographic QCD' program [15][16][17] where a holographic dual with the properties of QCD is being constructed.…”

“…The effective action (1.7) is the Legendre-tranformed version of an Einstein-Maxwell-Dilaton (EMD) system, where only the time-component of the gauge potential is turned on, and expressed in terms of the conjugate variable ρ. This type of systems were studied in detail in [14,24,25]. For a non trivial potential there exist solutions with hyperscaling-violating metric and Lifshitz scaling, as well as a log-behaved dilaton.…”

“…The definition of the ADM mass is given in terms of the trace of the extrinsic curvature for a radial slice of a constant-t surface, Θ = 1 √ grr ∂ r log g d−1 xx evaluated at a large cutoff 13) with the solution describing a field theory at temperature T from (3.11). The regularized quantity 14) JHEP04 (2014)042 corresponds to the regularized internal energy. The factor √ f is included to ensure that the geometries being compared have the same euclidean time periodicity.…”

On attractor mechanism ofAdS4black holes

“…Recently, a class of exact AdS 4 black hole solutions was obtained [6], though in that work a different method was used (see also [7,8,9,10,11]). Our solutions are more general and are of particular interest to clarifying aspects of the AdS/CMT correspondence because they can provide information about distinct holographic phases of matter [12]. Also, they can be useful in the context of fake supergravity [13].…”