Ground state and collective excitations of extended anyons

Nico Kirchner, Frank Pollmann, Technische Universität München

Simon Trebst, Eddy Ardonne, Adrian E. Feiguin +3 more

We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry end points we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.

Carlo A. Trugenberger

Carlo A. Trugenberger

We study the free anyon fluid by extending the usual Bogoliubov approximation to the case of nonlocal "statistical" interactions. We thereby compute the ground-state energy, the spectrum of low-lying excitations, the static structure factor, and the pair distribution function. The ground-state energy depends crucially on the magnetic dimension of the anyons, a scale that is unavoidably present at the quantum level. The linearly dispersing collective mode in the excitation spectrum indicates superfluidity.

Diptiman Sen

Hideaki Hiro-Oka

It is shown that the uniform ground state of ideal anyon gas can be constructed in the large-N collective field formalism and the excitation spectrum is given. It indicates that the system has a massless mode. In this treatment we employ a new set of gauge invariant variables to bypass the singularity which inevitably exists in the conventional density-phase variables. We also discuss the system of anyons including the delta function potential. The collective solution corresponding to Jackiw and Pi soliton is constructed.