Vortex Glass is a Metal: Unified Theory of the Magnetic Field and Disorder-Tuned Bose Metals

We consider the disordered quantum rotor model in the presence of a magnetic field. We analyze the transport properties in the vicinity of the multicritical point between the superconductor, phase glass and paramagnetic phases. We find that the magnetic field leaves metallic transport of bosons in the glassy phase in tact. In the vicinity of the vicinity of the superconductivity-to-Bose metal transition, the resistitivy turns on as $(H-H_c)^{2}$ with $H_c$. This functional form is in excellent agreement with the experimentally observed turn-on of the resistivity in the metallic state in MoGe, namely $R\approx R_c(H-H_c)^\mu$, $1<\mu<3$. The metallic state is also shown to presist in three spatial dimensions. In addition, we also show that the metallic state remains intact in the presence of Ohmic dissipation in spite of recent claims to the contrary. As the phase glass in $d=3$ is identical to the vortex glass, we conclude that the vortex glass is, in actuality, a metal rather than a superconductor at T=0. Our analysis unifies the recent experiments on vortex glass systems in which the linear resistivity remained non-zero below the putative vortex glass transition and the experiments on thin films in which a metallic phase has been observed to disrupt the direct transition from a superconductor to an insulator.Comment: Published version with an appendix showing that the claim in cond-mat/0510380 (and cond-mat/0606522) that Ohmic dissipation in the phase glass leads to a superconducting state is false. A metal persists in this case as wel

On the sign of kurtosis near the QCD critical point

We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. As a consequence, the kurtosis of a fluctuating observable, such as, e.g., proton multiplicity, may become smaller than the value given by independent Poisson statistics. We discuss implications for the Beam Energy Scan program at RHIC.Comment: 4 pages, 2 figure

Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire

We study the low-energy quantum electrodynamics of electrons and holes, in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p_T, where p_T is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest-order in (p/p_T), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound-states, and we calculate the dispersion law of such modes. We also compute the DC conductivity per unit length at zero chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.Comment: 7 pages, 2 figures. Definitive version, accepted for publication on Phys. Rev.

The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does {\it not}. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.Comment: 9 pages, 2 figure

Width of the longitudinal magnon in the vicinity of the O(3) quantum critical point

We consider a three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point separating the magnetically ordered and the magnetically disordered phases. A specific example is TlCuCl$_3$ where the quantum phase transition can be driven by hydrostatic pressure and/or by external magnetic field. As expected two transverse and one longitudinal magnetic excitation have been observed in the pressure driven magnetically ordered phase. According to the experimental data, the longitudinal magnon has a substantial width, which has not been understood and has remained a puzzle. In the present work, we explain the mechanism for the width, calculate the width and relate value of the width with parameters of the Bose condensate of magnons observed in the same compound. The method of an effective quantum field theory is employed in the work.Comment: 6 pages, 3 figure

Quantum critical scaling behavior of deconfined spinons

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to N=2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $\eta$ for the decay of the two-spin correlation function to first-order in $\epsilon=4-d$. We also note the scaling relation $\eta=d+2(1-\phi/\nu)$ connecting the exponent $\eta$ for the decay to the correlation length exponent $\nu$ and the crossover exponent $\phi$.Comment: 4.1 pages, no figures, references added; Version accepted for publication in PRB (RC

Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR

Critical exponents of the O(N) model in the infrared limit from functional renormalization

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.Comment: final version, 7 pages 7 figures, to appear in Phys. Rev.

Spin dynamics across the superfluid-insulator transition of spinful bosons

Bosons with non-zero spin exhibit a rich variety of superfluid and insulating phases. Most phases support coherent spin oscillations, which have been the focus of numerous recent experiments. These spin oscillations are Rabi oscillations between discrete levels deep in the insulator, while deep in the superfluid they can be oscillations in the orientation of a spinful condensate. We describe the evolution of spin oscillations across the superfluid-insulator quantum phase transition. For transitions with an order parameter carrying spin, the damping of such oscillations is determined by the scaling dimension of the composite spin operator. For transitions with a spinless order parameter and gapped spin excitations, we demonstrate that the damping is determined by an associated quantum impurity problem of a localized spin excitation interacting with the bulk critical modes. We present a renormalization group analysis of the quantum impurity problem, and discuss the relationship of our results to experiments on ultracold atoms in optical lattices.Comment: 43 pages (single-column format), 8 figures; v2: corrected discussion of fixed points in Section V

Galilean invariance and homogeneous anisotropic randomly stirred flows

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the Physical Review