Subir Sachdev

Hidden Fermi surfaces in compressible states of gauge-gravity duality

General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, z, and a specic hyperscaling violation exponent, . The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. (arXiv:1111.1023). We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconned gauge elds.

Gapless spin-fluid ground state in a random quantum Heisenberg magnet.

We examine the spin-S quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to SU(M) symmetry and studying the large M limit. For large S the ground state is a spin glass, while quantum fluctuations produce a spin-fluid state for small S. The spin-fluid phase is found to be generically gapless---the average, zero temperature, local dynamic spin susceptibility obeys \ensuremath{\chi}\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\omega})\ensuremath{\sim}ln(1/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert})+i(\ensuremath{\pi}/2)sgn(\ensuremath{\omega}) at low frequencies.

Deconfined quantum critical points.

The theory of second-order phase transitions is one of the foundations of modern statistical mechanics and condensed-matter theory. A central concept is the observable order parameter, whose nonzero average value characterizes one or more phases. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. We show that near second-order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm, and we present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional “confining” order parameters. Nevertheless, the critical theory contains an emergent gauge field and “deconfined” degrees of freedom associated with fractionalization of the order parameters. We propose that this paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems and offer a new perspective on the properties of complex materials.

Quantum critical transport, duality, and M-theory

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) Rcurrents can be obtained in the large N limit by applying the AdS/CFT correspondence to Mtheory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a “holographic self duality” in the large N limit, and perhaps more generally.

Quantum criticality: competing ground states in low dimensions

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial emergent excitations that control the physics over a significant portion of the phase diagram. Nonzero temperature dynamic properties near quantum critical points are described, using simple theoretical models. Possible quantum phases and transitions in the two-dimensional electron gas on a square lattice are discussed.

Radiation-induced magnetoresistance oscillations in a 2D electron gas

Recent measurements of a 2D electron gas subjected to microwave radiation reveal a magnetoresistance with an oscillatory dependence on the ratio of radiation frequency to cyclotron frequency. We perform a diagrammatic calculation and find radiation-induced resistivity oscillations with the correct period and phase. Results are explained via a simple picture of current induced by photoexcited disorder-scattered electrons. The oscillations increase with radiation intensity, easily exceeding the dark resistivity and resulting in negative-resistivity minima. At high intensity, we identify additional features, likely due to multiphoton processes, which have yet to be observed experimentally.

Condensed Matter and AdS/CFT

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

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.

Weak magnetism and non-Fermi liquids near heavy-fermion critical points

This paper is concerned with the weak-moment magnetism in heavy-fermion materials and its relation to the non-Fermi liquid physics observed near the transition to the Fermi liquid. We explore the hypothesis that the primary fluctuations responsible for the non-Fermi liquid physics are those associated with the destruction of the large Fermi surface of the Fermi liquid. Magnetism is suggested to be a low-energy instability of the resulting small Fermi surface state. A concrete realization of this picture is provided by a fractionalized Fermi liquid state which has a small Fermi surface of conduction electrons, but also has other exotic excitations with interactions described by a gauge theory in its deconfined phase. Of particular interest is a three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a U(1) gauge structure. A direct second-order transition from this state to the conventional Fermi liquid is possible and involves a jump in the electron Fermi surface volume. The critical point displays non-Fermi liquid behavior. A magnetic phase may develop from a spin density wave instability of the spinon Fermi surface. This exotic magnetic metal may have a weak ordered moment although the local moments do not participate in the Fermi surface. Experimental signatures of this phase and implications for heavy-fermion systems are discussed.

Ising and Spin orders in Iron-Based Superconductors

Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors