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

ON THERMODYNAMICS OF MULTISPECIES ANYONS

We address the problem of multispecies anyons, i.e. particles of different species whose wave function is subject to anyonlike conditions. The cluster and virial coefficients are considered. Special attention is paid to the case of anyons in the lowest Landau level of a strong magnetic field, when it is possible (i) to prove microscopically the equation of state, in particular in terms of Aharonov-Bohm charge-flux composite systems, and (ii) to formulate the problem in terms of single-state statistical distributions.Comment: Latex, 19 page

Is there an attraction between spinons in the Haldane--Shastry model?

While the Bethe Ansatz solution of the Haldane--Shastry model appears to suggest that the spinons represent a free gas of half-fermions, Bernevig, Giuliano, and Laughlin (BGL) (cond-mat/0011069, cond-mat/0011270) have concluded recently that there is an attractive interaction between spinons. We argue that the dressed scattering matrix obtained with the asymptotic Bethe Ansatz is to be interpreted as the true and physical scattering matrix of the excitations, and hence, that the result by BGL is inconsistent with an earlier result by Essler (cond-mat/9406081). We critically re-examine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane--Shastry model

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.

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

Extended Poincar\'e supersymmetry in three dimensions and supersymmetric anyons

We classify the unitary representations of the extended Poincar\'e supergroups in three dimensions. Irreducible unitary representations of any spin can appear, which correspond to supersymmetric anyons. Our results also show that all irreducible unitary representations necessarily have physical momenta. This is in sharp contrast to the ordinary Poincar\'e group in three dimensions, that admits in addition irreducible unitary representations with non-physical momenta, which are discarded on physical grounds.Comment: 7 pages; commentaries added in Sect. IV A and in Conclusion; added reference

Anthropic Explanation of the Dark Matter Abundance

I use Bousso's causal diamond measure to make a statistical prediction for the dark matter abundance, assuming an axion with a large decay constant f_a >> 10^{12} GeV. Using a crude approximation for observer formation, the prediction agrees well with observation: 30% of observers form in regions with less dark matter than we observe, while 70% of observers form in regions with more dark matter. Large values of the dark matter ratio are disfavored by an elementary effect: increasing the amount of dark matter while holding fixed the baryon to photon ratio decreases the number of baryons inside one horizon volume. Thus the prediction is rather insensitive to assumptions about observer formation in universes with much more dark matter than our own. The key assumption is that the number of observers per baryon is roughly independent of the dark matter ratio for ratios near the observed value.Comment: 10 pages; v3: published version, references adde

Nonequilibrium Approach to Bloch-Peierls-Berry Dynamics

We examine the Bloch-Peierls-Berry dynamics under a classical nonequilibrium dynamical formulation. In this formulation all coordinates in phase space formed by the position and crystal momentum space are treated on equal footing. Explicitly demonstrations of the no (naive) Liouville theorem and of the validity of Darboux theorem are given. The explicit equilibrium distribution function is obtained. The similarities and differences to previous approaches are discussed. Our results confirm the richness of the Bloch-Peierls-Berry dynamics

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.Comment: 4 pages; Add detailed discussion of feasibility of the scheme;add ref