14 research outputs found
Adventures in Holographic Dimer Models
We abstract the essential features of holographic dimer models, and develop
several new applications of these models. First, semi-holographically coupling
free band fermions to holographic dimers, we uncover novel phase transitions
between conventional Fermi liquids and non-Fermi liquids, accompanied by a
change in the structure of the Fermi surface. Second, we make dimer vibrations
propagate through the whole crystal by way of double trace deformations,
obtaining nontrivial band structure. In a simple toy model, the topology of the
band structure experiences an interesting reorganization as we vary the
strength of the double trace deformations. Finally, we develop tools that would
allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard
model.Comment: 22 pages, 8 figures; v2: brief description of case of pure D5 lattice
added in sec.3; v3: minor typo fixed; v4: minor change
Holographic Aspects of Fermi Liquids in a Background Magnetic Field
We study the effects of an external magnetic field on the properties of the
quasiparticle spectrum of the class of 2+1 dimensional strongly coupled
theories holographically dual to charged AdS black holes at zero
temperature. We uncover several interesting features. At certain values of the
magnetic field, there are multiple quasiparticle peaks representing a novel
level structure of the associated Fermi surfaces. Furthermore, increasing
magnetic field deforms the dispersion characteristics of the quasiparticle
peaks from non-Landau toward Landau behaviour. At a certain value of the
magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid,
the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed
non-separable solutions to infinite-sum solution
Landau Levels, Magnetic Fields and Holographic Fermi Liquids
We further consider a probe fermion in a dyonic black hole background in
anti-de Sitter spacetime, at zero temperature, comparing and contrasting two
distinct classes of solution that have previously appeared in the literature.
Each class has members labeled by an integer n, corresponding to the n-th
Landau level for the fermion. Our interest is the study of the spectral
function of the fermion, interpreting poles in it as indicative of
quasiparticles associated with the edge of a Fermi surface in the
holographically dual strongly coupled theory in a background magnetic field H
at finite chemical potential. Using both analytical and numerical methods, we
explicitly show how one class of solutions naturally leads to an infinite
family of quasiparticle peaks, signaling the presence of a Fermi surface for
each level n. We present some of the properties of these peaks, which fall into
a well behaved pattern at large n, extracting the scaling of Fermi energy with
n and H, as well as the dispersion of the quasiparticles.Comment: 23 pages, 4 figures. Changed some of the terminology: non-separable
-> infinite-sum. Clarified the relationship between our ansatz and the
separable ansat
Deconstructing holographic liquids
We argue that there exist simple effective field theories describing the
long-distance dynamics of holographic liquids. The degrees of freedom
responsible for the transport of charge and energy-momentum are Goldstone
modes. These modes are coupled to a strongly coupled infrared sector through
emergent gauge and gravitational fields. The IR degrees of freedom are
described holographically by the near-horizon part of the metric, while the
Goldstone bosons are described by a field-theoretical Lagrangian. In the cases
where the holographic dual involves a black hole, this picture allows for a
direct connection between the holographic prescription where currents live on
the boundary, and the membrane paradigm where currents live on the horizon. The
zero-temperature sound mode in the D3-D7 system is also re-analyzed and
re-interpreted within this formalism.Comment: 21 pages, 2 figure
Magnetic Field Induced Quantum Criticality via new Asymptotically AdS_5 Solutions
Using analytical methods, we derive and extend previously obtained numerical
results on the low temperature properties of holographic duals to
four-dimensional gauge theories at finite density in a nonzero magnetic field.
We find a new asymptotically AdS_5 solution representing the system at zero
temperature. This solution has vanishing entropy density, and the charge
density in the bulk is carried entirely by fluxes. The dimensionless magnetic
field to charge density ratio for these solutions is bounded from below, with a
quantum critical point appearing at the lower bound. Using matched asymptotic
expansions, we extract the low temperature thermodynamics of the system. Above
the critical magnetic field, the low temperature entropy density takes a simple
form, linear in the temperature, and with a specific heat coefficient diverging
at the critical point. At the critical magnetic field, we derive the scaling
law s ~ T^{1/3} inferred previously from numerical analysis. We also compute
the full scaling function describing the region near the critical point, and
identify the dynamical critical exponent: z=3.
These solutions are expected to holographically represent boundary theories
in which strongly interacting fermions are filling up a Fermi sea. They are
fully top-down constructions in which both the bulk and boundary theories have
well known embeddings in string theory.Comment: 50 page
Non-relativistic metrics from back-reacting fermions
It has recently been pointed out that under certain circumstances the
back-reaction of charged, massive Dirac fermions causes important modifications
to AdS_2 spacetimes arising as the near horizon geometry of extremal black
holes. In a WKB approximation, the modified geometry becomes a non-relativistic
Lifshitz spacetime. In three dimensions, it is known that integrating out
charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons
terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to
a gravitational and Maxwell Chern-Simons theory with a cosmological constant.
Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact
solutions to a fully back-reacted theory containing Dirac fermions in three and
four dimensions. We work out the dynamical exponent in terms of the fermion
mass and generalize this result to arbitrary dimensions.Comment: 26 pages, v2: typos corrected, references added, minor change
Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
We study the evolution and scaling of the entanglement entropy after two
types of quenches for a 2+1 field theory, using holographic techniques. We
study a thermal quench, dual to the addition of a shell of uncharged matter to
four dimensional Anti-de Sitter (AdS_4) spacetime, and study the subsequent
formation of a Schwarzschild black hole. We also study an electromagnetic
quench, dual to the addition of a shell of charged sources to AdS_4, following
the subsequent formation of an extremal dyonic black hole. In these backgrounds
we consider the entanglement entropy of two types of geometries, the infinite
strip and the round disc, and find distinct behavior for each. Some of our
findings naturally supply results analogous to observations made in the
literature for lower dimensions, but we also uncover several new phenomena,
such as (in some cases) a discontinuity in the time derivative of the
entanglement entropy as it nears saturation, and for the electromagnetic
quench, a logarithmic growth in the entanglement entropy with time for both the
disc and strip, before settling to saturation.Comment: 30 pages, 19 figures. Corrected typos and added some discussion. To
appear in New J. Phy
Black hole determinants and quasinormal modes
We derive an expression for functional determinants in thermal spacetimes as
a product over the corresponding quasinormal modes. As simple applications we
give efficient computations of scalar determinants in thermal AdS, BTZ black
hole and de Sitter spacetimes. We emphasize the conceptual utility of our
formula for discussing `1/N' corrections to strongly coupled field theories via
the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde
A conical deficit in the AdS4/CFT3 correspondence
Inspired by the AdS/CFT correspondence we propose a new duality that allow
the study of strongly coupled field theories living in a 2+1 conical
space-time. Solving the 4-d Einstein equations in the presence of an infinite
static string and negative cosmological constant we obtain a conical AdS4
space-time whose boundary is identified with the 2+1 cone found by Deser,
Jackiw and 't Hooft. Using the AdS4/CFT3 correspondence we calculate retarded
Green's functions of scalar operators living in the cone.Comment: v3, 14 pages. We reinterpret our results for the Green's functions in
the con
Strange metals and the AdS/CFT correspondence
I begin with a review of quantum impurity models in condensed matter physics,
in which a localized spin degree of freedom is coupled to an interacting
conformal field theory in d = 2 spatial dimensions. Their properties are
similar to those of supersymmetric generalizations which can be solved by the
AdS/CFT correspondence; the low energy limit of the latter models is described
by a AdS2 geometry. Then I turn to Kondo lattice models, which can be described
by a mean- field theory obtained by a mapping to a quantum impurity coupled to
a self-consistent environment. Such a theory yields a 'fractionalized Fermi
liquid' phase of conduction electrons coupled to a critical spin liquid state,
and is an attractive mean-field theory of strange metals. The recent
holographic description of strange metals with a AdS2 x R2 geometry is argued
to be related to such mean-field solutions of Kondo lattice models.Comment: 19 pages, 4 figures; Plenary talk at Statphys24, Cairns, Australia,
July 2010; (v2) added refs; (v3) more ref