Entanglement entropy of integer Quantum Hall states in polygonal domains

The entanglement entropy of the integer Quantum Hall states satisfies the area law for smooth domains with a vanishing topological term. In this paper we consider polygonal domains for which the area law acquires a constant term that only depends on the angles of the vertices and we give a general expression for it. We study also the dependence of the entanglement spectrum on the geometry and give it a simple physical interpretation.Comment: 8 pages, 6 figure

Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices

The frustrated spin-one-half Heisenberg model on triangualr and Kagome Lattices is mapped onto a single specis of fermion carrying statistical flux. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to be massive. This provides a new motivation for the spin-liquid Kalmeyer-Laughlin wave function. Good overlap of this wave function with the numerical ground state is found for small clusters.Comment: 13 pages, revtex. IUCM-920

Dirac, Anderson, and Goldstone on the Kagome

We show that there exists a long-range RVB state for the kagome lattice spin-1/2 Heisenberg antiferromagnet for which the spinons have a massless Dirac spectrum. By considering various perturbations of the RVB state which give mass to the fermions by breaking a symmetry, we are able to describe a wide-ranging class of known states on the kagome lattice, including spin-Peierls solid and chiral spin liquid states. Using an RG treatment of fluctuations about the RVB state, we propose yet a different symmetry breaking pattern and show how collective excitations about this state account for the gapless singlet modes seen experimentally and numerically. We make further comparison with numerics for Chern numbers, dimer-dimer correlation functions, the triplet gap, and other quantities. To accomplish these calculations, we propose a variant of the SU(N) theory which enables us to include many of the effects of Gutzwiller projection at the mean-field level.Comment: 18 pages, 6 figures; added references, minor correction

Entanglement Entropy for Singular Surfaces

We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.Comment: 66 pages,4 figures. Some typos are removed and a reference is adde

Electroweak Physics for Color Superconductivity

We construct the effective theories describing the electroweak interactions for the low energy excitations associated with the color superconductive phases of QCD at high matter density. The main result, for the 3 flavor case, is that the quasiparticle Goldstone boson $\pi^0$ decay into two physical massless photons is identical to the zero density case once we use the new Goldstone decay constant and the modified electric charge $\widetilde{e}=e \cos\theta$, with $\tan\theta =2e/\sqrt{3}g_s$ and $g_s$ the strong coupling constant. For 2 flavors we find that the coupling of the quarks to the neutral vector boson $Z^0$ is modified with respect to the zero density case. We finally point out possible applications of our result to the physics of compact objects.Comment: 23 pages, 1 Figure, RevTex. More discussion and references adde

Order and quantum phase transitions in the cuprate superconductors

It is now widely accepted that the cuprate superconductors are characterized by the same long-range order as that present in the Bardeen-Cooper-Schrieffer (BCS) theory: that associated with the condensation of Cooper pairs. We argue that many physical properties of the cuprates require interplay with additional order parameters associated with a proximate Mott insulator. We review a classification of Mott insulators in two dimensions, and contend that the experimental evidence so far shows that the class appropriate to the cuprates has collinear spin correlations, bond order, and confinement of neutral, spin S=1/2 excitations. Proximity to second-order quantum phase transitions associated with these orders, and with the pairing order of BCS, has led to systematic predictions for many physical properties. We use this context to review the results of recent neutron scattering, fluxoid detection, nuclear magnetic resonance, and scanning tunnelling microscopy experiments.Comment: 20 pages, 13 figures, non-technical review article; some technical details in the companion review cond-mat/0211027; (v3) added refs; (v4) numerous improvements thanks to the referees, to appear in Reviews of Modern Physics; (v6) final version as publishe

Non-zero temperature transport near quantum critical points

We describe the nature of charge transport at non-zero temperatures ($T$) above the two-dimensional ($d$) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order $k_B T/\hbar$. This implies that the transport at frequencies $\omega \ll k_B T/\hbar$ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while $\omega \gg k_B T/\hbar$ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be $e^2 / h$ times a non-trivial universal scaling function of $\hbar \omega / k_B T$, and not independent of $\hbar \omega/k_B T$, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $\hbar \omega/k_B T \to 0$ limit of this function, and is a universal number times $e^2 / h$, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless $\hbar \omega/k_B T \to \infty$ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times $e^2 / h$. We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in $\epsilon=3-d$. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.Comment: Feedback incorporated into numerous clarifying remarks; additional appendix discusses relationship to transport in dissipative quantum mechanics and quantum Hall edge state tunnelling problems, stimulated by discussions with E. Fradki

Effects of dissipation on quantum phase transitions

We discuss the effect of dissipation on quantum phase transitions. In particular we concentrate on the Superconductor to Insulator and Quantum-Hall to Insulator transitions. By invoking a phenomenological parameter $\alpha$ to describe the coupling of the system to a continuum of degrees of freedom representing the dissipative bath, we obtain new phase diagrams for the quantum Hall and superconductor-insulator problems. Our main result is that, in two-dimensions, the metallic phases observed in finite magnetic fields (possibly also strictly zero field) are adiabatically deformable from one to the other. This is plausible, as there is no broken symmetry which differentiates them.Comment: 13 pages, 4 figure

Hint for Quintessence-like Scalars from Holographic Dark Energy

We use the generalized holographic dark energy model, in which both the cosmological constant (CC) and Newton's constant G_N are scale-dependent, to set constraints on the renormalization-group (RG) evolution of both quantities phrased within quantum field theory (QFT) in a curved background. Considering the case in which the energy-momentum tensor of ordinary matter stays individually conserved, we show from the holographic dark energy requirement that the RG laws for the CC and G_N are completely determined in terms of the lowest part of the particle spectrum of an underlying QFT. From simple arguments one can then infer that the lowest-mass fields should have a Compton wavelength comparable with the size of the current Hubble horizon. Hence, although the models with the variable CC (or with both the CC and the G_N varying) are known tolead to successful cosmologies without introducing a new light degree of freedom, we nonetheless find that holography actually brings us back to the quintessence proposal. An advantage of having two different components of the vacuum energy in the cosmological setting is also briefly mentioned.Comment: 9 pages, two references added, to appear in JCA