Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.Comment: (v2) A typo in Fig. 1 and a slight error in Eq. (4) corrected; all the main results and conclusions remain unchange

Some Calculable Contributions to Entanglement Entropy

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry; its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.Comment: 4+ pages, 1 figure. v2: Some clarifications and more references; updated to resemble version published in PR

Confinement and the quark Fermi-surface in SU(2N) QCD-like theories

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrated by means of a simple quark model.Comment: 5 pages, 2 figures, revised journal versio

Scaling of the superconducting transition temperature in underdoped high-Tc cuprates with a pseudogap energy: Does this support the anyon model of their superfluidity?

In earlier work, we have been concerned with the scaling properties of some classes of superconductors, specifically with heavy Fermion materials and with five bcc transition metals of BCS character. Both of these classes of superconductors were three-dimensional but here we are concerned solely with quasi-two-dimensional high-Tc cuprates in the underdoped region of their phase diagram. A characteristic feature of this part of the phase diagram is the existence of a pseudogap (pg). We therefore build our approach around the assumption that kB Tc / E_pg is the basic dimensionless ratio on which to focus, where the energy E_pg introduced above is a measure of the pseudogap. Since anyon fractional statistics apply to two-dimensional assemblies, we expect the fractional statistics parameter allowing `interpolation' between Fermi-Dirac and Bose-Einstein statistical distribution functions as limiting cases to play a significant role in determining kB Tc / E_pg and experimental data are analyzed with this in mind.Comment: Phys. Chem. Liquids, to be publishe

Asymptotic Freedom: From Paradox to Paradigm

Asymptotic freedom was developed as a response to two paradoxes: the weirdness of quarks, and in particular their failure to radiate copiously when struck; and the coexistence of special relativity and quantum theory, despite the apparent singularity of quantum field theory. It resolved these paradoxes, and catalyzed the development of several modern paradigms: the hard reality of quarks and gluons, the origin of mass from energy, the simplicity of the early universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2: typo (in Ohm's law) correcte

Generalized Aharonov-Bohm effect, homotopy classes and Hausdorff dimension

We suggest as gedanken experiment a generalization of the Aharonov-Bohm experiment, based on an array of solenoids. This experiment allows in principle to measure the decomposition into homotopy classes of the quantum mechanical propagator. This yields information on the geometry of the average path of propagation and allows to determine its Hausdorff dimension.Comment: 14 pages, LaTeX + 3 figures, P

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.Comment: 13 pages, no figures, Phyzz

Quark Mass Textures and sin 2 beta

Recent precise measurements of sin 2 beta from the B-factories (BABAR and BELLE) and a better known strange quark mass from lattice QCD make precision tests of predictive texture models possible. The models tested include those hierarchical N-zero textures classified by Ramond, Roberts and Ross, as well as any other hierarchical matrix Ansatz with non-zero 12 = 21 and vanishing 11 and 13 elements. We calculate the maximally allowed value for sin 2 beta in these models and show that all the aforementioned models with vanishing 11 and 13 elements are ruled out at the 3 sigma level. While at present sin 2 beta and |Vub/Vcb| are equally good for testing N-zero texture models, in the near future the former will surpass the latter in constraining power.Comment: 1+20 pages, 2 figures, JHEP3 clas

The strong-CP question in SU(3)_c X SU(3)_L X U(1)_N models

We analyze two recent models based on the gauge group SU(3)$_c\times$SU(3)$_L\times$U(1)$_N$ where each generation is not anomaly-free, but anomaly cancels when three generations are taken into account. We show that the most general Yukawa couplings of these models admit of a Peccei-Quinn symmetry. This symmetry can be extended to the entire Lagrangian by using extra fields in a very elegant way so that the resulting axion can be made invisible.Comment: Latex, 8 pages, no figure

Systematic Study Of Leptonic Mixing In A Class Of SU_H(2) Models

We perform a systematic analysis of the PMNS matrices which arise when one assigns the three generations of leptons to the $2\oplus 1$ representation of a horizontal $SU_H(2)$ symmetry. This idea has been previously explored by Kuchimanchi and Mohapatra. However, we assume $(i)$ the neutrino mass matrix results from leptonic couplings to $SU_L(2)$ triplet scalar fields and $(ii)$ hierarchies exist amongst lepton mass matrix elements which result from couplings to scalar fields with different $SU_H(2)$ charges. Of the sixteen candidate PMNS matrices which result it is found that only one is both predictive and possesses a leading order structure compatible with experimental data. The relevant neutrino mass matrix displays the symmetry $L_e-L_\mu-L_\tau$ to leading order and we explore the perturbations required to produce a realistic lepton spectrum. The effective mass in neutrinoless double beta decay is required to lie in the range $/(10^{-2}\mathrm{eV})\in[0.7,2.5]$, which is just below current experimental bounds. $U_{e3}$ is non-zero but not uniquely determined.Comment: To appear in Phys. Rev.