Fractional dimensional Fock space and Haldane's exclusion statistics. q/p case

TL;DR

This paper extends the concept of fractional dimensional Hilbert spaces and Haldane exclusion statistics from rational to irrational statistical parameters, constructing the associated statistical mechanics and exploring applications in strongly correlated systems.

Contribution

It generalizes Haldane's exclusion statistics to rational and irrational parameters, providing a framework for statistical mechanics of such particles.

Findings

Extended fractional Hilbert spaces to rational and irrational g

Constructed statistical mechanics for these particles

Discussed applications to Hubbard and t-J models

Abstract

The discussion of Fractional dimensional Hilbert spaces in the context of Haldane exclusion statistics is extended from the case \cite{IG} of $g=1/p$ for the statistical parameter to the case of rational $g=q/p$ with $q,p$-coprime positive integers. The corresponding statistical mechanics for a gas of such particles is constructed. This procedure is used to define the statistical mechanics for particles with irrational $g$. Applications to strongly correlated systems such as the Hubbard and $t-J$ models are discussed.