Dissecting holographic conductivities

The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic current relaxation. This decomposition is different from those previously proposed, and is consistent with the known hydrodynamic properties in the translationally invariant limit. This is the first step towards constructing a consistent theory of charged hydrodynamics with slow momentum relaxation.Comment: v2: minor edits, matches published version. v1: 26 pages, 1 figur

Momentum dissipation and effective theories of coherent and incoherent transport

We study heat transport in two systems without momentum conservation: a hydrodynamic system, and a holographic system with spatially dependent, massless scalar fields. When momentum dissipates slowly, there is a well-defined, coherent collective excitation in the AC heat conductivity, and a crossover between sound-like and diffusive transport at small and large distance scales. When momentum dissipates quickly, there is no such excitation in the incoherent AC heat conductivity, and diffusion dominates at all distance scales. For a critical value of the momentum dissipation rate, we compute exact expressions for the Green's functions of our holographic system due to an emergent gravitational self-duality, similar to electric/magnetic duality, and SL(2,R) symmetries. We extend the coherent/incoherent classification to examples of charge transport in other holographic systems: probe brane theories and neutral theories with non-Maxwell actions.Comment: v1: 41 pages + appendices, 7 figures. v2: references and clarifications added. v3: reference adde

Incoherent transport in clean quantum critical metals

In a clean quantum critical metal, and in the absence of umklapp, most d.c. conductivities are formally infinite due to momentum conservation. However, there is a particular combination of the charge and heat currents which has a finite, universal conductivity. In this paper, we describe the physics of this conductivity $\sigma_Q$ in quantum critical metals obtained by charge doping a strongly interacting conformal field theory. We show that it satisfies an Einstein relation and controls the diffusivity of a conserved charge in the metal. We compute $\sigma_Q$ in a class of theories with holographic gravitational duals. Finally, we show how the temperature scaling of $\sigma_Q$ depends on certain critical exponents characterizing the quantum critical metal. The holographic results are found to be reproduced by the scaling analysis, with the charge density operator becoming marginal in the emergent low energy quantum critical theory.Comment: v1: 1 + 16 pages + reference

Hydrodynamic flows of non-Fermi liquids: magnetotransport and bilayer drag

We consider a hydrodynamic description of transport for generic two dimensional electron systems that lack Galilean invariance and do not fall into the category of Fermi liquids. We study magnetoresistance and show that it is governed only by the electronic viscosity provided that the wavelength of the underlying disorder potential is large compared to the microscopic equilibration length. We also derive the Coulomb drag transresistance for double-layer non-Fermi liquid systems in the hydrodynamic regime. As an example, we consider frictional drag between two quantum Hall states with half-filled lowest Landau levels, each described by a Fermi surface of composite fermions coupled to a $U(1)$ gauge field. We contrast our results to prior calculations of drag of Chern-Simons composite particles and place our findings in the context of available experimental data.Comment: 4 pages + references + supplementary information, 1 figur

Holographic duality and the resistivity of strange metals

We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting, locally quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to the electronic entropy.Comment: v2: 20 pages; changed order of presentation and added background information; emphasised local criticalit

AdS/CFT and Landau Fermi liquids

We study the field theory dual to a charged gravitational background in which the low temperature entropy scales linearly with the temperature. We exhibit the existence of a sound mode which is described by hydrodynamics, even at energies much larger than the temperature, and explain how this, and other properties of the field theory, are consistent with those of a (3+1)-dimensional Landau Fermi liquid, finely tuned to the Pomeranchuk critical point. We also discuss how one could engineer a higher-derivative gravitational Lagrangian which reproduces the correct low temperature behavior of shear viscosity in a generic Landau Fermi liquid.Comment: harvmac, 35 pages, 2 figures. v2: minor changes and references adde

Thermal diffusivity and chaos in metals without quasiparticles

We study the thermal diffusivity $D_T$ in models of metals without quasiparticle excitations (`strange metals'). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infra-red fixed points $D_T$ is always related to parameters characterizing many-body quantum chaos: the butterfly velocity $v_B$, and Lyapunov time $\tau_L$ through $D_T \sim v_B^2 \tau_L$. The relationship holds independently of the charge density, periodic potential strength or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime, and is otherwise insensitive to the profile of any matter fields.Comment: 27 page

Hydrodynamic theory of quantum fluctuating superconductivity

A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effective field theoretic and fully quantum -- derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a `hydrodynamic supercyclotron' resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this `topologically ordered superfluid vortex liquid' is determined by the conductivities of the normal component of the liquid. Our work gives a controlled framework for low temperature metallic phases arising from phase-disordered superconductivity.Comment: 1 + 44 pages. 2 figures. v2 discussion improved in places. v3 sign errors fixed in section

Hydrodynamics of cold holographic matter

We show that at any temperature, the low-energy (with respect to the chemical potential) collective excitations of the transverse components of the energy-momentum tensor and the global U(1) current in the field theory dual to the planar RN-AdS4 black hole are simply those of hydrodynamics. That is, hydrodynamics is applicable even at energy scales much greater than the temperature. It is applicable even at zero temperature. Specifically, we find that there is always a diffusion mode with diffusion constant proportional to the ratio of entropy density to energy density. At low temperatures, the leading order momentum and temperature dependences of the dispersion relation of this mode are controlled by the dimension of an operator in the thermal CFT1 dual to the near-horizon Schwarzschild-AdS2 geometry.Comment: 36 pages, 4 figures, v2: published version, minor clarifications and references adde

Holographic zero sound at finite temperature

We use gauge-gravity duality to study the temperature dependence of the zero sound mode and the fundamental matter diffusion mode in the strongly coupled {\cal N}=4 SU(N_c) supersymmetric Yang-Mills theory with N_f {\cal N}=2 hypermultiplets in the N_c>>1, N_c>>N_f limit, which is holographically realized via the D3/D7 brane system. In the high density limit \mu>>T, three regimes can be identified in the behavior of these modes, analogous to the collisionless quantum, collisionless thermal and hydrodynamic regimes of a Landau Fermi-liquid. The transitions between the three regimes are characterized by the parameters T/\mu and (T/\mu)^2 respectively, and in each of these regimes the modes have a distinctively different temperature and momentum dependence. The collisionless-hydrodynamic transition occurs when the zero sound poles of the density-density correlator in the complex frequency plane collide on the imaginary axis to produce a hydrodynamic diffusion pole. We observe that the properties characteristic of a Landau Fermi-liquid zero sound mode are present in the D3/D7 system despite the atypical T^6/\mu^3 temperature scaling of the specific heat and an apparent lack of a directly identifiable Fermi surface.Comment: 35 pages, 13 figures, 2 tables, 3 animation