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Physical review. B, Condensed matter

Haldane liquid with mutual exclusion statistics

Kazumoto Iguchi

Published May 15, 2000• 7 citations

Abstract

I study basic properties of a Haldane liquid with mutual exclusion statistics (MES), which is a liquid of quasiparticles interacting only through the MES that are assumed to be parameters as usually done in the definition of Haldane statistics. By this approximation for the statistics, I obtain the following: The ground state of the system has multiple pseudo--Fermi surfaces for all species of quasiparticles when $T=0,$ where the pseudo--Fermi surface for each species exhibits the particle-hole asymmetry. I define the dressed energies so as to satisfy the Sutherland-Wu (SW) functional equations that are the defining relations for the MES, from which the elementary excitations near the ground state are given. And finally, I show that the SW equations have an unusual type of duality such as spin-charge duality in the system.

DOI: 10.1103/physrevb.61.12757

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I study basic properties of a Haldane liquid with mutual exclusion statistics (MES), which is a liquid of quasiparticles interacting only through the MES that are assumed to be parameters as usually done in the definition of Haldane statistics. By this approximation for the statistics, I obtain the following: The ground state of the system has multiple pseudo--Fermi surfaces for all species of quasiparticles when

T=0,

where the pseudo--Fermi surface for each species exhibits the particle-hole asymmetry. I define the dressed energies so as to satisfy the Sutherland-Wu (SW) functional equations that are the defining relations for the MES, from which the elementary excitations near the ground state are given. And finally, I show that the SW equations have an unusual type of duality such as spin-charge duality in the system.

We study in this paper the properties of a many body system of fermions obeying exclusion-statistics (Haldane liquid) where the origin of exclusion statistics is coming from an interaction-induced displacement field

\mathbf{a}_{\mathbf{k}}

introduced by Sutherland (Haldane-Sutherland liquid). In particular we show how the Luttinger Theorem becomes compatible with exclusion statistics as a result of momentum conservation and adiabaticity. As a result, the low energy properties of Haldane-Sutherland liquids are Fermi/Luttinger liquid-like.

We discuss how one-dimensional interacting fermion systems, which in the low-energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication, the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum variables the Landau parameters of the generalized Fermi fluid can be transformed to zero. This change in interaction is compensated by a change of the entropy function, which is consistent with the interpretation of the quasiparticles as satisfying generalized exclusion statistics.

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite-temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticles enables us to predict the energies of the ground and excited states of the N-body system. PACS Nos.: 05.30-d, 73.20Dx

We determine the exclusion statistics properties of the fundamental edge quasiparticles over a specific $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ non-Abelian quantum Hall state known as the

q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

Pfaffian state. The fundamental excitations are the edge electrons of charge $\ensuremath{-}e$ and the edge quasiholes of charge

+e/4

. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics as described by F. D. M. Haldane.