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Physical Review Letters

Finite-size studies of semion systems

X. C. Xie, Song He, S. Das Sarma

Published Jul 30, 1990• 23 citations
Publisher

Abstract

The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations in a spherical geometry. It is shown that Laughlin's mean-field theory gives an accurate description of the ground-state properties of the finite, spherical system. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long-wavelength limit, and predict a novel roton minimum at a finite value of the wave number q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.

DOI
10.1103/physrevlett.65.649

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Physical Review Letters•Jan 21, 1985•448 citations
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations in a spherical geometry. It is shown that Laughlin's mean-field theory gives an accurate description of the ground-state properties of the finite, spherical system. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long-wavelength limit, and predict a novel roton minimum at a finite value of the wave number q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation in a spherical geometry. It is shown that Laughlin's mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.
The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation In a spherical geometry. It is shown that Laughlin`s mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.
We study a tight-binding model for anyons on a square lattice using a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value. For any anyon density per site ${\mathrm{\ensuremath{\rho}}}_{0}$=p/q and statistics \ensuremath{\nu}=1-1/n, the anyon system has a linear collective mode if and only if q is greater than twice the largest common factor of p and n. The collective mode dispersion, \ensuremath{\omega}(k), is calculated numerically for n=1 (hard-core bosons) and n=2 (semions) at certain densities.
The ground-state properties of particles obeying fractional statistics, on lattices with spherical topology, are studied numerically. The possible existence of superfluidity in semion systems is examined by studies of pairing energies, flux quantization, and the effects of applied magnetic fields. Evidence of superfluidity is observed, in agreement with previous numerical studies on cylindrical topologies. Comparison of the results for these different topologies allows some conclusions to be made about finite-size and boundary effects. In particular, we argue that there is no constant shift in the flux-quantization values.
The incompressible states of interacting two-dimensional electrons in a high magnetic field has been studied by finite-size calculations in the spherical geometry. The excitation spectrum at 13\frac{1}{3}31​ Landau-level filling is described, and the Laughlin-Jastrow character of the Coulomb-interaction ground state is unambiguously confirmed. As the interaction is varied, a transition to a gapless compressible state is observed.