Anyons in a magnetic field

Johnson, Michael D.; Canright, Geoffrey

doi:10.1103/physrevb.41.6870

Cited by 89 publications

(56 citation statements)

References 24 publications

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“…The eigenvalue problem (8.20) is identical to the two anyon problem in a constant B field with the statistics parameter being proportional to the energy value E. So, for the energy levels E n,m we obtain ( [42][43][44])…”

Section: Nonconfined Motionmentioning

confidence: 99%

From Gauging Nonrelativistic Translations to N-Body Dynamics

Lukierski

Stichel²,

Zakrzewski

2001

Annals of Physics

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We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gaugeinvariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d = 2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in * e-mail: lukier@ift.uni.wroc.pl † email: pstichel@gmx.de ‡ e-mail: W.J.Zakrzewski@durham.ac.uk 1 time) translations and rigid rotations. We describe the effective interaction of the d = 2 N -particle problem and discuss its classical solution for N = 2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H = H( x, p; H) which implies, after quantization, a nonstandard form of the Schrödinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r ≤ r 0 ) and the scattering states with continuum energy correspond to the classical motion for r > r 0 . We extend our considerations by introducing an external constant magnetic field and, for N = 2, provide the classical and quantum solutions in the confined and unconfined regimes.

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Section: Nonconfined Motionmentioning

confidence: 99%

From Gauging Nonrelativistic Translations to N-Body Dynamics

Lukierski

Stichel²,

Zakrzewski

2001

Annals of Physics

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“…In practice, a Hall insulator can be realized with or without magnetic field. Since anyons in a strong magnetic field have been studied before [18][19][20][21] , in this article we consider the quantum anomalous Hall(QAH) system without Landau levels, which has been proposed theoretically 24,26 and realized in recent experiments 27 . To be specific we take the fermion Lagrangian L M as a 2D massive Dirac fermion with N f flavors, which can be written conveniently in the Euclidean space-time as…”

Section: Rpa Calculationmentioning

confidence: 99%

Hall effect, edge states, and Haldane exclusion statistics in two-dimensional space

Marchetti

et al. 2015

Phys. Rev. B

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We clarify the relation between two kinds of statistics for particle excitations in planar systems: the braid statistics of anyons and the Haldane exclusion statistics(HES). It is shown non-perturbatively that the HES exists for incompressible anyon liquid in the presence of a Hall response. We also study the statistical properties of a specific quantum anomalous Hall model with Chern-Simons term by perturbation in both compressible and incompressible regimes, where the crucial role of edge states to the HES is shown.

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“…As an extension to initial embedded atom method (EAM) [13,14] and analytical EAM (AEAM, developed by Johnson and co-workers [15][16][17][18]), the modified analytical EAM (MAEAM) has been used successfully to study the properties of metals and alloys [19][20][21]. In the MAEAM, the total energy E t of a system is expressed as [21]:…”

Section: Calculation Methodsmentioning

confidence: 99%