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$_4$ 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

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

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

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

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

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

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

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