Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study

It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion response computed by the emergent quantum critical IR, even when the potential becomes relevant in the infra-red. However, in the regime where holographic quasi-particles occur, defining a Fermi surface in the continuum, they acquire a finite lifetime at any finite potential strength. At the transition from irrelevancy to relevancy of the Bianchi potential in the deep infra-red the quasi-particle remnants disappear completely and the fermion spectrum exhibits a purely relaxational behaviour.Comment: 30 pages, 10 figure

Trace anomalies and the string-inspired definition of quantum-mechanical path integrals in curved space

We consider quantum-mechanical path integrals for non-linear sigma models on a circle defined by the string-inspired method of Strassler, where one considers periodic quantum fluctuations about a center-of-mass coordinate. In this approach one finds incorrect answers for the local trace anomalies of the corresponding $n$-dimensional field theories in curved space. The quantum field theory approach to the quantum-mechanical path-integral, where quantum fluctuations are not periodic but vanish at the endpoints, yields the correct answers. We explain these results by a detailed analysis of general coordinate invariance in both methods. Both approaches can be derived from the same operator expression and the integrated trace anomalies in both schemes agree. In the string-inspired method the integrands are not invariant under general coordinate transformations and one is therefore not permitted to use Riemann normal coordinates.Comment: LaTeX, 12 pages, 17 figure

Extracting New Physics from the CMB

We review how initial state effects generically yield an oscillatory component in the primordial power spectrum of inflationary density perturbations. These oscillatory corrections parametrize unknown new physics at a scale $M$ and are potentially observable if the ratio $H_{infl}/M$ is sufficiently large. We clarify to what extent present and future CMB data analysis can distinguish between the different proposals for initial state corrections.Comment: Invited talk by B. Greene at the XXII Texas Symposium on Relativistic Astrophysics, Stanford University, 13-17 December 2004, (TSRA04-0001), 8 pages, LaTeX, some references added, added paragraph at the end of section 2 and an extra note added after the conclusions regarding modifications to the large k power spectra deduced from galaxy survey

Holographic fermions in external magnetic fields

We study the Fermi level structure of 2+1-dimensional strongly interacting electron systems in external magnetic field using the AdS/CFT correspondence. The gravity dual of a finite density fermion system is a Dirac field in the background of the dyonic AdS-Reissner-Nordstrom black hole. In the probe limit the magnetic system can be reduced to the non-magnetic one, with Landau-quantized momenta and rescaled thermodynamical variables. We find that at strong enough magnetic fields, the Fermi surface vanishes and the quasiparticle is lost either through a crossover to conformal regime or through a phase transition to an unstable Fermi surface. In the latter case, the vanishing Fermi velocity at the critical magnetic field triggers the non-Fermi liquid regime with unstable quasiparticles and a change in transport properties of the system. We associate it with a metal-"strange metal" phase transition. Next we compute the DC Hall and longitudinal conductivities using the gravity-dressed fermion propagators. For dual fermions with a large charge, many different Fermi surfaces contribute and the Hall conductivity is quantized as expected for integer Quantum Hall Effect (QHE). At strong magnetic fields, as additional Fermi surfaces open up, new plateaus typical for the fractional QHE appear. The somewhat irregular pattern in the length of fractional QHE plateaus resemble the outcomes of experiments on thin graphite in a strong magnetic field. Finally, motivated by the absence of the sign problem in holography, we suggest a lattice approach to the AdS calculations of finite density systems.Comment: 34 pages, 14 figure

Ultrafast dynamics of cold Fermi gas after a local quench

We consider non-equilibrium dynamics of two initially independent reservoirs $A$ and $B$ filled with a cold Fermi gas coupled and decoupled by two quantum quenches following one another. We find that the von Neumann entropy production induced by the quench is faster than thermal transport between the reservoirs and defines the short-time dynamics of the system. We analyze the energy change in the system which adds up the heat transferred between $A$ and $B$ and the work done by the quench to uncouple the reservoirs. In the case when $A$ and $B$ interact for a short time, we notice an energy increase in both reservoirs upon decoupling. This energy gain results from the quench's work and does not depend on the initial temperature imbalance between the reservoirs. We relate the quench's work to the mutual correlations of $A$ and $B$ expressed through their von Neumann entropies. Utilizing this relation, we show that once $A$ and $B$ become coupled, their entropies grow (on a timescale of the Fermi time) faster than the heat flow within the system. This result may provide a track of quantum correlations' generation at finite temperatures which one may probe in ultracold atoms, where we expect the characteristic timescale of correlations' growth to be $\sim 0.1 {\rm ms}$.Comment: 12 pages, 6 figures (published version