Estimate of crossed-boson-exchange contributions to the binding energy of two-body systems

Binding energies calculated from using the Bethe-Salpeter equation in the simplest ladder approximation significantly differ from those obtained in the non-relativistic standard instantaneous approximation. While they should a priori be better, they turn out to be further away from an exact calculation in the case of scalar neutral particles or from experiment in the case of the Coulomb interaction. Part of the discrepancy is due to the omission in the interaction kernel of contributions corresponding to crossed-boson-exchange diagrams. The role of these contributions is examined numerically, using a simple approximation. The sensitivity to both the coupling constant and the mass of the exchanged boson is considered.Comment: 11 pages, 7 figures, file.ta

Braiding non-Abelian quasiholes in fractional quantum Hall states

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the $\mathbb{Z}_3$ Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the $\mathbb{Z}_3$ Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the non-unitary Gaffnian wave function.Comment: 9 pages, 9 figures; published versio

Matrix product state representation of non-Abelian quasiholes

We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions with conformal-block normalization and monodromy, and complements the matrix product state representation of fractional quantum Hall ground states.Comment: 14 pages, 2 figures; published versio

Phase transitions for a collective coordinate coupled to Luttinger liquids

We study various realizations of collective coordinates, e.g. the position of a particle, the charge of a Coulomb box or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids (LL) with N flavors. We find that for Luttinger parameter 1/2<K<1 there is a phase transition from a delocalized phase into a phase with a periodic potential at strong coupling. In the delocalized phase the dynamics is dominated by an effective mass, i.e. diffusive in imaginary time, while on the transition line it becomes dissipative. At K=1/2 there is an additional transition into a localized phase with no diffusion at zero temperature.Comment: 5 pages, 2 figures, 1 table, Phys. Rev. Lett. (in press