142 research outputs found
Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes
We review a recent holographic analysis arXiv:1005.4690 of charged black
holes with scalar hair in view of their applications to the cuprate high
temperature superconductors. We show in particular that these black holes show
an interesting phase structure including critical behaviour at zero temperature
or charge, describe both conductors and insulators (including holographic
Mott-like insulators), generically have no residual entropy and exhibit
experimentally observed scaling relations between electronic entropy, specific
heat and (linear) DC resistivity. Transport properties are discussed in the
companion contribution to these proceedings.Comment: 6 pages, 6 figures, to appear in "Proceedings of the XVIth European
Workshop on String Theory", Madrid, June 2010, to be published in Fortsch.
Phy
Effective holographic theory of charge density waves
We use gauge/gravity duality to write down an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. We first focus on the leading two-derivative action, which leads to excited states with nonzero strain. We show that including subleading quartic derivative terms leads to dynamical instabilities of AdS2 translation invariant states and to stable phases breaking translations spontaneously. We compute analytically the real part of the electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating
Entangled Dilaton Dyons
Einstein-Maxwell theory coupled to a dilaton is known to give rise to
extremal solutions with hyperscaling violation. We study the behaviour of these
solutions in the presence of a small magnetic field. We find that in a region
of parameter space the magnetic field is relevant in the infra-red and
completely changes the behaviour of the solution which now flows to an
attractor. As a result there is an extensive ground state
entropy and the entanglement entropy of a sufficiently big region on the
boundary grows like the volume. In particular, this happens for values of
parameters at which the purely electric theory has an entanglement entropy
growing with the area, , like which is believed to be a
characteristic feature of a Fermi surface. Some other thermodynamic properties
are also analysed and a more detailed characterisation of the entanglement
entropy is also carried out in the presence of a magnetic field. Other regions
of parameter space not described by the end point are also
discussed.Comment: Some comments regarding comparison with weakly coupled Fermi liquid
changed, typos corrected and caption of a figure modifie
Universal scaling properties of extremal cohesive holographic phases
We show that strongly-coupled, translation-invariant holographic IR phases at
finite density can be classified according to the scaling behaviour of the
metric, the electric potential and the electric flux introducing four critical
exponents, independently of the details of the setup. Solutions fall into two
classes, depending on whether they break relativistic symmetry or not. The
critical exponents determine key properties of these phases, like thermodynamic
stability, the (ir)relevant deformations around them, the low-frequency scaling
of the optical conductivity and the nature of the spectrum for electric
perturbations. We also study the scaling behaviour of the electric flux through
bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and
characterize the deviation from the Ryu-Takayanagi prescription in terms of the
critical exponents.Comment: v4: corrected a typo in eqn (3.29), now (3.28). Conclusions unchange
Phase transition and hyperscaling violation for scalar Black Branes
We investigate the thermodynamical behavior and the scaling symmetries of the
scalar dressed black brane (BB) solutions of a recently proposed, exactly
integrable Einstein-scalar gravity model [1], which also arises as
compactification of (p-1)-branes with a smeared charge. The extremal, zero
temperature, solution is a scalar soliton interpolating between a conformal
invariant AdS vacuum in the near-horizon region and a scale covariant metric
(generating hyperscaling violation on the boundary field theory)
asymptotically. We show explicitly that for the boundary field theory this
implies the emergence of an UV length scale (related to the size of the brane),
which decouples in the IR, where conformal invariance is restored. We also show
that at high temperatures the system undergoes a phase transition. Whereas at
small temperature the Schwarzschild-AdS BB is stable, above a critical
temperature the scale covariant, scalar-dressed BB solution, becomes
energetically preferred. We calculate the critical exponent z and the
hyperscaling violation parameter of the scalar-dressed phase. In particular we
show that the hyperscaling violation parameter is always negative. We also show
that the above features are not a peculiarity of the exact integrable model of
Ref.[1], but are a quite generic feature of Einstein-scalar and
Einstein-Maxwell-scalar gravity models for which the squared-mass of the scalar
field is positive and the potential vanishes exponentially as the scalar field
goes to minus infinity.Comment: 20 pages, 4 figures. In the revised version it has been pointed out
that the Einstein-scalar gravity model considered in the paper also arises as
compactification of black p-branes with smeared charge
Charged Dilatonic AdS Black Branes in Arbitrary Dimensions
We study electromagnetically charged dilatonic black brane solutions in
arbitrary dimensions with flat transverse spaces, that are asymptotically AdS.
This class of solutions includes spacetimes which possess a bulk region where
the metric is approximately invariant under Lifshitz scalings. Given fixed
asymptotic boundary conditions, we analyze how the behavior of the bulk up to
the horizon varies with the charges and derive the extremality conditions for
these spacetimes.Comment: References update
Spatially modulated instabilities of geometries with hyperscaling violation
We perform a study of possible instabilities of the infrared AdS(2) x R-2 region of solutions to Einstein-Maxwell-dilaton systems which exhibit an intermediate regime of hyperscaling violation and Lifshitz scaling. Focusing on solutions that are magnetically charged, we probe the response of the system to spatially modulated fluctuations, and identify regions of parameter space in which the infrared AdS(2) geometry is unstable to perturbations. The conditions for the existence of instabilities translate to restrictions on the structure of the gauge kinetic function and scalar potential. In turn, these can lead to restrictions on the dynamical critical exponent z and on the amount of hyperscaling violation theta. Our analysis thus provides further evidence for the notion that the true ground state of 'scaling' solutions with hyperscaling violation may be spatially modulated phases
Non-conformal Hydrodynamics in Einstein-dilaton Theory
In the Einestein-dilaton theory with a Liouville potential parameterized by
, we find a Schwarzschild-type black hole solution. This black hole
solution, whose asymptotic geometry is described by the warped metric, is
thermodynamically stable only for . Applying the gauge/gravity
duality, we find that the dual gauge theory represents a non-conformal thermal
system with the equation of state depending on . After turning on the
bulk vector fluctuations with and without a dilaton coupling, we calculate the
charge diffusion constant, which indicates that the life time of the quasi
normal mode decreases with . Interestingly, the vector fluctuation with
the dilaton coupling shows that the DC conductivity increases with temperature,
a feature commonly found in electrolytes.Comment: 27 pages and 2 figures, published in JHE
Schr\"odinger Holography with and without Hyperscaling Violation
We study the properties of the Schr\"odinger-type non-relativistic holography
for general dynamical exponent z with and without hyperscaling violation
exponent \theta. The scalar correlation function has a more general form due to
general z as well as the presence of \theta, whose effects also modify the
scaling dimension of the scalar operator. We propose a prescription for minimal
surfaces of this "codimension 2 holography," and demonstrate the (d-1)
dimensional area law for the entanglement entropy from (d+3) dimensional
Schr\"odinger backgrounds. Surprisingly, the area law is violated for d+1 < z <
d+2, even without hyperscaling violation, which interpolates between the
logarithmic violation and extensive volume dependence of entanglement entropy.
Similar violations are also found in the presence of the hyperscaling
violation. Their dual field theories are expected to have novel phases for the
parameter range, including Fermi surface. We also analyze string theory
embeddings using non-relativistic branes.Comment: 62 pages and 6 figures, v2: several typos in section 5 corrected,
references added, v3: typos corrected, references added, published versio
The holographic quantum effective potential at finite temperature and density
We develop a formalism that allows the computation of the quantum effective
potential of a scalar order parameter in a class of holographic theories at
finite temperature and charge density. The effective potential is a valuable
tool for studying the ground state of the theory, symmetry breaking patterns
and phase transitions. We derive general formulae for the effective potential
and apply them to determine the phase transition temperature and density in the
scaling region.Comment: 27 page
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