We study the scaling behavior of the entanglement entropy of two-dimensional conformal quantum critical systems, i.e., systems with scale-invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that under quite general conditions, the entanglement entropy of a large and simply connected subsystem of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a dwave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N , quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a "bunching" effect, while for higher states in the Jain sequences they should exhibit an "anti-bunching" effect.The classification of fundamental particles in terms of their quantum statistics, Bose-Einstein (bosons) and Fermi-Dirac (fermions), is a fundamental law of Nature enshrined in the Principles of Quantum Mechanics. In the form of the Spin-Statistics Theorem it is also one of the basic axioms of Quantum Field Theory (and String Theory as well). However, it has long been known that other types of quantum statistics are also possible if the physical system has a reduced dimensionality. Indeed, the possible existence of anyons [1,2], particles with fractional or braid statistics, interpolating between bosons and fermions, is one of the most startling predictions of Quantum Mechanics in two space dimensions.The best experimental candidates for anyons presently known are the vortices (or quasiparticles (qp)) of a strongly interacting 2D electron gas (2DEG) in a strong magnetic field in the FQH regime [3,4,5,6,7]. In this regime, the 2DEG behaves as an incompressible dissipationless topological fluid exhibiting the FQH effect [3,4]. The quasiparticles of FQH fluids have remarkable properties [4,5,6,7]: they are finite energy vortices (or solitons) which carry fractional charge and fractional (braid) statistics. Although by now there is strong experimental evidence for fractional charge [8,9,10,11,12], similar evidence is still lacking for fractional statistics (such experimental evidence has been reported very recently [13].)There are two ways to think about statistics. A first way is through the concept of braiding (fractional) statistics, in which the two particle wave function Ψ(r 1 , r 2 ) acquires a statistical angle θ upon an adiabatic exchange process, Ψ(r 1 , r 2 ) = e iθ Ψ(r 2 , r 1 ).(1)For fractional statistics to occur, the statistical angle θ should take values intermediate between that of bosons (θ = 0, particles commute) and fermions (θ = π, particles anti-commute) [2,7]. The other way is to consider, in a finite size system, the effect of the presence of particles to the subsequent addition of another particle. The Pauli Exclusion Principle dictates that each fermion in a system reduces the available states to add extra fermions by 1. In contrast, the presence of a boson does not affect the later addition of bosons at all. The natural consequence of the presence of an anyon is an intermediate effect, i.e. a generalized exclusion p...

We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors ν ∼ 1 the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter K, leading to the appearance of a zero-bias differential conductance peak of magnitude Gt = Ke 2 /h at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value ν * 1, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage V , the crossover scale TK , and the temperature T . The low height of the zero bias peak ∼ 0.1e 2 /h observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for ν 2 can be explained as an effect caused by spin reversed electrons, i. e. if the 2DEG is assumed to have a small polarization near ν ∼ 2. We also predict that as the temperature is lowered ν * should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for ν 2.

We study the interplay between charge and spin ordering in electronic liquid crystalline states with a particular emphasis on fluctuating spin stripe phenomena observed in recent neutron scattering experiments. Based on a phenomenological model, we propose that charge nematic ordering is indeed behind the formation of temperature dependent incommensurate inelastic peaks near wave vector (pi, pi) in the dynamic structure factor of YBa(2)Cu(3)O(6+y). We strengthen this claim by providing a compelling fit to the experimental data.