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arXiv:cond-mat/9411125 · Physical review. B, Condensed matter

Universality classes, statistical exclusion principle, and properties of interacting fermions

Krzysztof Byczuk, Józef Spałek

Published Mar 15, 1995• 14 citations
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Abstract

We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi- or Luttinger-liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger, and spin liquids) represents a universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.

DOI
10.1103/physrevb.51.7934

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We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi- or Luttinger-liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger, and spin liquids) represents a universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.
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We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems kkk-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable kkk-Fermi liquid models with spin-charge separation are discussed as examples.
U(1)U(1)U(1) Fermi liquid theory - A Fermi liquid state that supports exclusion statistics
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The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.
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