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arXiv:cond-mat/9512037

Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition

Yasuhiro Hatsugai, Mahito Kohmoto, Tohru Koma, Yong-Shi Wu

Published Dec 6, 1995• 0 citations
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Abstract

We study statistical characterization of the many-body states in the exactly solvable model with internal degree of freedom in more than one dimension. The model exhibits the Mott metal-insulator transition. It is shown that the ground state is described by that of a generalized ideal gas of particles (called exclusons) which have mutual exclusion statistics between different species. In addition to giving a perspective view of spin-charge separation, the model constitutes an explicit example of mutual exclusion statistics in more than two dimensions.

DOI
10.48550/arxiv.cond-mat/9512037

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We study statistical characterization of the many-body states in the exactly solvable model with internal degree of freedom in more than one dimension. The model exhibits the Mott metal-insulator transition. It is shown that the ground state is described by that of a generalized ideal gas of particles (called exclusons) which have mutual exclusion statistics between different species. In addition to giving a perspective view of spin-charge separation, the model constitutes an explicit example of mutual exclusion statistics in more than two dimensions.
We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chains, the Hubbard chain, and a model in higher dimensions which exhibits the Mott metal-insulator transition. It is shown that the ground states of these systems are all described by that of a generalized ideal gas of particles (called exclusons) which have mutual-exclusion statistics, either between different rapidities or between different species. For the Bethe ansatz solvable models, the low-temperature properties are well described by the excluson description if the degeneracies due to string solutions with complex rapidities are taken into account correctly. For the Hubbard chain with strong but finite coupling, charge-spin separation is shown for thermodynamics at low temperatures. Moreover, we present an exactly solvable model in arbitrary dimensions which, in addition to giving a perspective view of spin-charge separation, constitutes an explicit example of mutual-exclusion statistics in more than two dimensions. \textcopyright{} 1996 The American Physical Society.
We show that the Hubbard model with infinite-range Coulomb coupling is equivalent to an ideal gas of three species of particles obeying fractional exclusion statistics. A full appreciation of this mapping requires an extension of the pertinent formalism. This very simple, but rather peculiar model is exactly solvable in any dimension and exhibits a Mott metal-insulator transition, whose universality class is shown to be that of a free spinless Fermi gas. A modified version of the Luttinger theorem is shown to apply in any dimension. We also characterize the metallic and insulating phases by obtaining the electronic band structure as well as the interacting density of states. The fractional statistics manifests itself on the amplitudes of several thermodynamic quantities and, in particular, the Pauli spin susceptibility is subdominant in all metallic phases, and a Curie-type of response appears.
We consider the SU(N) generalization of the one-dimensional Hubbard model with arbitrary degeneracy N (spin and orbital degrees of freedom). This model is integrable and has several unusual properties at low temperatures. The Bethe-Ansatz equations at T=0 are analyzed in the thermodynamic limit in the absence of external fields. In the continuum limit, the effective interaction between the charge degrees of freedom corresponds to a potential of the form [sinh(ax)${]}^{\mathrm{\ensuremath{-}}2}$, where x is the distance between the particles involved and a is an inverse length scale. In the limit N\ensuremath{\rightarrow}\ensuremath{\infty} and in the continuum limit, the charges reduce to a Bose gas interacting via a \ensuremath{\delta}-function potential. We further address here the properties of the charge degrees of freedom for a band filling close to one electron per site. The charge excitations obey Fermi statistics. We find a Mott metal-insulator transition at a critical value Uc{\mathit{U}}_{\mathit{c}}Uc​ of the Coulomb repulsion. Uc{\mathit{U}}_{\mathit{c}}Uc​ depends on N (Uc{\mathit{U}}_{\mathit{c}}Uc​=0 for N=2). A qualitative change in the charge-rapidity distribution is found at Uc{\mathit{U}}_{\mathit{c}}Uc​. The Fermi velocity is finite for UUc{\mathit{U}}_{\mathit{c}}Uc​, diverges as U\ensuremath{\rightarrow}Uc{\mathit{U}}_{\mathit{c}}Uc​, and vanishes for U>Uc{\mathit{U}}_{\mathit{c}}Uc​.
Critical properties of transitions between a variety of quantum fluids and the Mott insulator are examined in terms of the transition to an incompressible state. In one dimension, they show universally common properties each other irrespective of the statistics, components and the interaction of particles. In two dimensions, they show qualitative differences originated from the differences in the nature of the quantum fluid. It is useful to categorize the singularity at the Mott transition into two types, namely, one characterized by the charge mass divergence and the other by the vanishment of the carrier number. This difference originates from the number of components. Its variety is further explored by examining various cases such as strongly correlated fermions, hard core bosons and boson t - J models. Critical properties to other incompressible states such as spin gap states and the fractional quantum Hall state are also discussed from the same viewpoint. Relevance of our analyses to the understanding of normal state properties in high- T c cuprates and other transition metal oxides is discussed.
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.