Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions

We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b species of complex bosons and N_f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large N_b and N_f, but for arbitrary values of the ratio N_b/N_f, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin-liquids, charge-liquids and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.Comment: 30 pages, 8 figure

Fermi surfaces and gauge-gravity duality

We give a unified overview of the zero temperature phases of compressible quantum matter: i.e. phases in which the expectation value of a globally conserved U(1) density, Q, varies smoothly as a function of parameters. Provided the global U(1) and translational symmetries are unbroken, such phases are expected to have Fermi surfaces, and the Luttinger theorem relates the volumes enclosed by these Fermi surfaces to . We survey models of interacting bosons and/or fermions and/or gauge fields which realize such phases. Some phases have Fermi surfaces with the singularities of Landau's Fermi liquid theory, while other Fermi surfaces have non-Fermi liquid singularities. Compressible phases found in models applicable to condensed matter systems are argued to also be present in models obtained by applying chemical potentials (and other deformations allowed by the residual symmetry at non-zero chemical potential) to the paradigmic supersymmetric gauge theories underlying gauge-gravity duality: the ABJM model in spatial dimension d=2, and the N=4 SYM theory in d=3.Comment: 40 pages, 13 figures; (v2) more complete phase diagram

Cosmogenic photons as a test of ultra-high energy cosmic ray composition

Although recent measurements of the shower profiles of ultra-high energy cosmic rays suggest that they are largely initiated by heavy nuclei, such conclusions rely on hadronic interaction models which have large uncertainties. We investigate an alternative test of cosmic ray composition which is based on the observation of ultra-high energy photons produced through cosmic ray interactions with diffuse low energy photon backgrounds during intergalactic propagation. We show that if the ultra-high energy cosmic rays are dominated by heavy nuclei, the flux of these photons is suppressed by approximately an order of magnitude relative to the proton-dominated case. Future observations by the Pierre Auger Observatory may be able to use this observable to constrain the composition of the primaries, thus providing an important cross-check of hadronic interaction models.Comment: 4 pages, 2 figure

Nonequilibrium Dynamics of the Complex Ginzburg-Landau Equation. I. Analytical Results

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau (CGL) equation. In particular, we characterize evolution morphologies using spiral defects. This paper (referred to as $\rm I$) is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of the Gaussian auxiliary field (GAF) ansatz in characterizing a multi-spiral morphology. In the next paper of this exposition (referred to as $\rm II$), we will present detailed numerical results.Comment: 21 pages, 7 figure

Occupation number and fluctuations in the finite-temperature Bose-Hubbard model

We study the occupation numbers and number fluctuations of ultra-cold atoms in deep optical lattices for finite temperatures within the Bose-Hubbard model. Simple analytical expressions for the mean occupation number and number fluctuations are obtained in the weak-hopping regime using an interpolation between results from different perturbation approaches in the Mott-insulator and superfluid phases. These analytical results are compared to exact one dimensional numerical calculations using a finite temperature variant of the Density-Matrix Renormalisation Group (DMRG) method and found to have a high degree of accuracy. We also find very good agreement in the crossover ``thermal'' region. With the present approach the magnitude of number fluctuations under realistic experimental conditions can be estimated and the properties of the finite temperature phase diagram can be studied.Comment: 4 pages, 1 eps figure, submitted to PR

Quantum Hall to Insulator Transition in the Bilayer Quantum Hall Ferromagnet

We describe a new phase transition of the bilayer quantum Hall ferromagnet at filling fraction $\nu = 1$. In the presence of static disorder (modeled by a periodic potential), bosonic $S=1/2$ spinons can undergo a superfluid-insulator transition while preserving the ferromagnetic order. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Physical consequences for charge and counterflow conductivity, and for interlayer tunneling conductance in the presence of quenched disorder are discussed.Comment: 4 pages, no figure

Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets

We describe the spin distribution in the vicinity of a non-magnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered Neel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1/2 (if the system without the impurity had an even number of S=1/2 spins), and recent numerical studies in a double layer antiferromagnet (K. H.Hoglund et al., cond-mat/0611418) have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a Neel state to a paramagnet with local spin singlets, in models with an even number of S=1/2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a Neel state to a valence bond solid, in antiferromagnets with a single S=1/2 spin per unit cell, which are described by a deconfined field theory of spinons.Comment: 30 pages, 9 figure

Compressible quantum phases from conformal field theories in 2+1 dimensions

Conformal field theories (CFTs) with a globally conserved U(1) charge Q can be deformed into compressible phases by modifying their Hamiltonian, H, by a chemical potential H -> H - \mu Q. We study 2+1 dimensional CFTs upon which an explicit S duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called `Bose metals' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solid, and the product of their magnetic charge and Q determines the area of the unit cell. We discuss implications for holographic theories on asymptotically AdS4 spacetimes: S duality and monopole/dyon fields play important roles in this connection.Comment: 30 pages, 2 figures; (v2) small corrections and more ref