Relativistic Quantum Information of Anyons
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Relativistic Quantum Information of Anyons Leili Esmaeilifar1 · Behrouz Mirza2 · Hosein Mohammadzadeh3 Received: 9 March 2020 / Accepted: 24 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, a method is developed to investigate the relativistic quantum information of anyons. Anyons are particles with intermediate statistics ranging between Bose-Einstein and Fermi-Dirac statistics, with a parameter α (0 < α < 1) characteristic of this intermediate statistics. A density matrix is also introduced as a combination of the density matrices of bosons and fermions with a continuous parameter, α, that represents the behavior of anyons. This density matrix reduces to bosonic and fermionic density matrices in the limits α → 0 and α → 1, respectively. We compute entanglement entropy, negativity, and coherency for anyons in non-inertial frames as a function of α. We also computed quantum fisher information for these particles. Semions, which are particles with α = 0.5, were found to have minimum quantum fisher information with respect to α than those with other values of fractional parameter. Keywords Anyons · Fractional statistics · Density matrix · Semions
1 Introduction Particles in the three-dimensional or higher space are classified, based on their statistical behavior, as bosons and fermions. The multi-particle wave function of identical bosons (fermions) is symmetric (antisymmetric) under interchange of any pair of particles. It has been shown that quasiparticles in the two-dimensional space may have intermediate Behrouz Mirza
[email protected] Leili Esmaeilifar [email protected] Hosein Mohammadzadeh [email protected] 1
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
2
Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran
3
Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
International Journal of Theoretical Physics
statistics between bosons and fermions with a continuous parameter. This can be written in the two particles’ case as follows: | ψ1 ψ2 = eiπα | ψ2 ψ1 ,
(1)
where, α is the fractional statistical exchange quantum number, also called the statistical parameter, ranging over 0 ≤ α ≤ 1, with α = 0 standing for bosons and α = 1 for fermions. The theoretical possibility of these particles was first propounded by J. M. Leinaas and J. Myrheim [1]. They later came to be called anyon by F. Wilczek [2]. The Pauli exclusion principle was generalized to yield another sort of generalized statistics introduced by F. D. M. Haldane [3]. This generalization is independent of the dimension of the system. A fractional parameter, g, was defined for the fractional exclusion statistics. In this exclusion statistics two limits are defined for g, where g = 0 (g=1) corresponds to bosons (fermions). Despite the radical differences in the basic definitions of the fractional exchange and fractional exclusion statistics, the rel
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