What can gauge-gravity duality teach us about condensed matter physics?

I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with non-zero temperature dynamics and transport are difficult to answer using conventional field theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality, and discuss the prospects for reliable computation of low frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality, and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly-coupled compressible quantum states.Comment: 34 pages, 11 figures + 16 pages of Supplementary Material with 4 figures; to appear in Annual Reviews of Condensed Matter Physics; (v2) add a figure, and clarifications; (v3) final version; (v4) small correction

Valence bond solid order near impurities in two-dimensional quantum antiferromagnets

Recent scanning tunnelling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states which are centered on a Cu-O-Cu bond (Kohsaka et. al., cond-mat/0703309). As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered Neel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: i) local modulation in the exchange constants, and ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The `boundary' critical theory for these classes is developed: in the second class we find a `VBS pinwheel' around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.Comment: 41 pages, 6 figures; (v2) Minor changes in terminology, added reference

Dynamics of a quantum phase transition in the random Ising model

A quantum phase transition from paramagnetic to ferromagnetic phase is driven by a time-dependent external magnetic field. For any rate of the transition the evolution is non-adiabatic and finite density of defects is excited in the ferromagnetic state. The density of excitations has only logarithmic dependence on the transition rate. This is much weaker than any usual power law scaling predicted for pure systems by the Kibble-Zurek mechanism.Comment: 4 pages and 2 figures; improved presentatio

Mean field dynamics of superfluid-insulator phase transition in a gas of ultra cold atoms

A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold atoms placed in an optical lattice is performed using the time dependent Gutzwiller mean field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Nature 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap.Comment: final version, correct Fig.7 (the published version contains wrong fig.7 by mistake

Metallic spin glasses

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite temperature phase diagram is described and crossover functions are computed in mean field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.Comment: Contribution to the Proceedings of the ITP Santa Barbara conference on Non-Fermi liquids, 25 pages, requires IOP style file

Bridging the Testing Speed Gap: Design for Delay Testability

The economic testing of high-speed digital ICs is becoming increasingly problematic. Even advanced, expensive testers are not always capable of testing these ICs because of their high-speed limitations. This paper focuses on a design for delay testability technique such that high-speed ICs can be tested using inexpensive, low-speed ATE. Also extensions for possible full BIST of delay faults are addresse

Itinerant-localized dual character of a strongly-correlated superfluid Bose gas in an optical lattice

We investigate a strongly-correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erdos to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band with a finite energy gap coexist. We also show that the rf-tunneling current measurement would give a useful information about the duality of a strongly-correlated superfluid Bose gas near the superfluid-insulator transition.Comment: 10 pages, 4 figure

A low-speed BIST framework for high-performance circuit testing

Testing of high performance integrated circuits is becoming increasingly a challenging task owing to high clock frequencies. Often testers are not able to test such devices due to their limited high frequency capabilities. In this article we outline a design-for-test methodology such that high performance devices can be tested on relatively low performance testers. In addition, a BIST framework is discussed based on this methodology. Various implementation aspects of this technique are also addresse