arXiv subjects

Nabil Iqbal

Publications and source records attributed to Nabil Iqbal.

49 records · Page 3Linked to original sources

arXiv2013

A Simple Holographic Model of Nonlinear Conductivity

We present a simple analytic gravitational solution which describes the holographic dual of a 2+1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study 1+1 and 3+1 dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.

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arXiv2013

Charge transport by holographic Fermi surfaces

We compute the contribution to the conductivity from holographic Fermi surfaces obtained from probe fermions in an AdS charged black hole. This requires calculating a certain part of the one-loop correction to a vector propagator on the charged black hole geometry. We find that the current dissipation is as efficient as possible and the transport lifetime coincides with the single-particle lifetime. In particular, in the case where the spectral density is that of a marginal Fermi liquid, the resistivity is linear in temperature.

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arXiv2012

Friedel oscillations and horizon charge in 1D holographic liquids

In many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger's theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.

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arXiv2012

Luttinger's theorem, superfluid vortices, and holography

Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. "fractionalized") charge degrees of freedom.

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arXiv2011

Lectures on holographic non-Fermi liquids and quantum phase transitions

In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: 1. Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? 2. Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high T_c cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid", which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.

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arXiv2011

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.

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arXiv2011

Holographic non-Fermi liquid fixed points

Techniques arising from string theory can be used to study assemblies of strongly-interacting fermions. Via this `holographic duality', various strongly-coupled many body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared fixed point theory which is represented by an AdS_2 region in the dual gravitational description. Here we describe in detail the gravity calculation of this IR correlation function. This article is a contribution to a special issue of Phil. Trans. A on the normal state of the cuprates; as such, we also provide some review and context.

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arXiv2010

Holography and the Coleman-Mermin-Wagner theorem

In 2+1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large thermal fluctuations of the order parameter. The holographic correspondence implies that analogous effects must also occur in 3+1 dimensional theories with gauged symmetries in certain curved spacetimes with horizon. By performing a one loop computation in the background of a holographic superconductor, we show that bulk quantum fluctuations wash out the classical order parameter at sufficiently large distance scales. The low temperature phase is seen to exhibit algebraic long range order. Beyond the specific example we study, holography suggests that IR singular quantum fluctuations of the fields and geometry will play an interesting role for many 3+1 dimensional asymptotically AdS spacetimes with planar horizon.

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arXiv2010

From black holes to strange metals

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

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arXiv2010

Quantum phase transitions in holographic models of magnetism and superconductors

We study a holographic model realizing an "antiferromagnetic" phase in which a global SU(2) symmetry representing spin is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions respectively.

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arXiv2009

Spatial correlators in strongly coupled plasmas

We numerically calculate the spatial correlators of the scalar and pseudoscalar operators $F^2$ and $F\tilde F$, in SU(3) Yang-Mills theory at zero and finite-temperature on the lattice. We compare the results over the distances $\frac{1}{2T}<r<\frac{3}{2T}$ to the free-field prediction, to the operator-product expansion as well as to the strongly coupled large-$N_c$ $\sN=4$ super-Yang-Mills theory, where results are obtained by AdS/CFT methods. For $T_c<T<1.15T_c$, both channels exhibit stronger spatial correlations than in the vacuum, and we give an explanation for this, using sum-rules and the operator-product expansion. The AdS/CFT calculation provides a semi-quantitatively successful description of the vacuum-subtracted $F^2$ correlator, renormalized in the 3-loop $\overline{\rm MS}$ scheme, in the interval of temperatures $1.2<T/T_c<1.9$, while the free-field prediction has the wrong sign. The $F\tilde F$ and $F^2$ correlators are predicted to have the same functional form both at weak coupling and in the strongly coupled SYM theory. The Yang-Mills plasma does not meet that expectation below $2T_c$. Instead we find that strong fluctuations of $F\tilde F$ are present at least up to that temperature. We discuss the impact of our results on our understanding of the quark-gluon plasma.

hep-lat↗

arXiv2009

Real-time response in AdS/CFT with application to spinors

We discuss a simple derivation of the real-time AdS/CFT prescription as an analytic continuation of the corresponding problem in Euclidean signature. We then extend the formalism to spinor operators and apply it to the examples of real-time fermionic correlators in CFTs dual to pure AdS and the BTZ black hole.

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arXiv2008

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm

We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the "membrane paradigm" fluid of classical black hole mechanics. Thus generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusion.

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