Mutual Exclusion Statistics in Exactly Solvable Models in One and Higher Dimensions at Low Temperatures

TL;DR

This paper explores the statistical nature of many-body states in exactly solvable models, revealing that their ground states can be described by a generalized ideal gas with mutual exclusion statistics, including in higher dimensions.

Contribution

It introduces a generalized exclusion statistics framework for exactly solvable models, including higher-dimensional systems, and demonstrates charge-spin separation in the Hubbard chain.

Findings

Ground states described by exclusons with mutual exclusion statistics

Charge-spin separation observed in the Hubbard chain at low temperatures

Explicit higher-dimensional model exhibiting mutual exclusion statistics

Abstract

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 chain, the Hubbard chain, and a model in higher dimensions which exhibits the Mott metal-insulator transition. It is shown that the ground state of these systems is 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.