On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy

The challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states (density operators). A family of tripartite states satisfying equality is derived.Comment: 8 pages; Latex2e and Revtex

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.Comment: RevTex, 4 pages, 1 ps figur

Finite temperature transport at the superconductor-insulator transition in disordered systems

I argue that the incoherent, zero-frequency limit of the universal crossover function in the temperature-dependent conductivity at the superconductor-insulator transition in disordered systems may be understood as an analytic function of dimensionality of system d, with a simple pole at d=1. Combining the exact result for the crossover function in d=1 with the recursion relations in d=1+\epsilon, the leading term in the Laurent series in the small parameter \epsilon for this quantity is computed for the systems of disordered bosons with short-range and Coulomb interactions. The universal, low-temperature, dc critical conductivity for the dirty boson system with Coulomb interaction in d=2 is estimated to be 0.69 (2e)^2 /h, in relatively good agreement with many experiments on thin films. The next order correction is likely to somewhat increase the result, possibly bringing it closer to the self-dual value.Comment: 9 pages, LaTex, no figure

Chiral symmetry breaking in QED3{\rm QED}_{3} in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\rm QED}_{3}$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure ${\rm QED}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\rm QED}_{3}$.Comment: 7 pages, 7 figure

Antiferromagnetism from phase disordering of a d-wave superconductor

The unbinding of vortex defects in the superconducting condensate with d-wave symmetry at T=0 is shown to lead to the insulator with incommensurate spin-density-wave order. The transition is similar to the spontaneous generation of the "chiral" mass in the three dimensional quantum electrodynamics, at which the global chiral symmetry one can define in the superconducting state is spontaneously broken. Other symmetry related states and possible relations to recent experiments on uderdoped cuprates are briefly discussed.Comment: RevTex, 4 pages, one ps figure; comments on confinement in the SDW added, references updated; final versio

Dual superfluid-Bose glass critical point in two dimensions and the universal conductivity

We study the continuum version of the dual theory for a system of two-dimensional, zero temperature, disordered bosons, interacting with short range repulsion and at a commensurate density. The dual theory, which describes vortices in the bosonic ground state, and has a form of 3D classical scalar electrodynamics in random, correlated magnetic field, admits a new disordered critical point within RG calculation at fixed dimension. The universal conductivity and the critical exponents at the superfluid-Bose glass critical point are calculated as series in fixed-point values of the dual coupling constants, to the lowest non-trivial order: $\sigma_c = 0.25 (2e)^2 /h$, $\nu=1.38$ and $z=1.93$. The comparison with numerical results and experiments is discussed.Comment: 8 pages, LaTex, some clarifications and references adde

Dual theory of the superfluid-Bose glass transition in disordered Bose-Hubbard model in one and two dimensions

I study the zero temperature phase transition between superfluid and insulating ground states of the Bose-Hubbard model in a random chemical potential and at large integer average number of particles per site. Duality transformation maps the pure Bose-Hubbard model onto the sine-Gordon theory in one dimension (1D), and onto the three dimensional Higgs electrodynamics in two dimensions (2D). In 1D the random chemical potential in dual theory couples to the space derivative of the dual field, and appears as a random magnetic field along the imaginary time direction in 2D. I show that the transition from the superfluid state in both 1D and 2D is always controlled by the random critical point. This arises due to a coupling constant in the dual theory with replicas which becomes generated at large distances by the random chemical potential, and represents a relevant perturbation at the pure superfluid-Mott insulator fixed point. At large distances the dual theory in 1D becomes equivalent to the Haldane's macroscopic representation of disordered quantum fluid, where the generated term is identified with random backscattering. In 2D the generated coupling corresponds to the random mass of the complex field which represents vortex loops. I calculate the critical exponents at the superfluid-Bose glass fixed point in 2D to be \nu=1.38 and z=1.93, and the universal conductivity at the transition \sigma_c = 0.26 e_{*}^2 /h, using the one-loop field-theoretic renormalization group in fixed dimension.Comment: 25 pages, 6 Postscript figures, LaTex, references updated, typos corrected, final version to appear in Phys. Rev. B, June 1, 199

Gauge dependenceof the order parameter anomalous dimension in the Ginzburg-Landau model and the critical fluctuations in superconductors

The critical fluctuations of superconductors are discussed in a fixed dimension scaling suited to describe the type II regime. The gauge dependence of the anomalous dimension of the scalar field is stablished exactly from the Ward-Takahashi identities. Its fixed point value gives the $\eta$ critical exponent and it is shown that $\eta$ is gauge independent, as expected on physical grounds. In the scaling considered, $\eta$ is found to be zero at 1-loop order, while $\nu\approx 0.63$. This result is just the 1-loop values for the XY model obtained in the fixed dimension renormalization group approach. It is shown that this XY behavior holds at all orders. The result $\eta=\eta_{XY}$ should be contrasted with the negative values frequently reported in the literature.Comment: EuroLaTex, 7 pages, 2 figures, reference updated; version to be published in Europhysics Letter

Hausdorff dimension of critical fluctuations in abelian gauge theories

The geometric properties of the critical fluctuations in abelian gauge theories such as the Ginzburg-Landau model are analyzed in zero background field. Using a dual description, we obtain scaling relations between exponents of geometric and thermodynamic nature. In particular we connect the anomalous scaling dimension $\eta$ of the dual matter field to the Hausdorff dimension $D_H$ of the critical fluctuations, {\it which are fractal objects}. The connection between the values of $\eta$ and $D_H$, and the possibility of having a thermodynamic transition in finite background field, is discussed.Comment: Accepted for publication in PR

Universality of conductivity in interacting graphene

The Hubbard model on the honeycomb lattice describes charge carriers in graphene with short range interactions. While the interaction modifies several physical quantities, like the value of the Fermi velocity or the wave function renormalization, the a.c. conductivity has a universal value independent of the microscopic details of the model: there are no interaction corrections, provided that the interaction is weak enough and that the system is at half filling. We give a rigorous proof of this fact, based on exact Ward Identities and on constructive Renormalization Group methods