Fractional statistics of charge carriers in the one- and two-dimensional t-J model. A hint for the cuprates?

TL;DR

This paper interprets the exact solutions of the one- and two-dimensional t-J models using fractional statistics, providing insights into the behavior of charge carriers and implications for high-temperature superconductors.

Contribution

It introduces a fractional statistics framework for charge carriers in the t-J model, linking microscopic constraints to macroscopic properties in cuprates.

Findings

Charge carriers exhibit fractional exchange and exclusion statistics.

Exclusion statistics arises from the no-double occupation constraint.

The formalism offers a new perspective on the properties of hole-doped cuprates.

Abstract

We show that we can interpret the exact solution of the one-dimensional t-J model in the limit of small J in terms of charge carriers with both exchange (braid) and exclusion (Haldane) statistics with parameter 1/2. We discuss an implementation of the same statistics in the two-dimensional t-J model, emphasizing similarities and differences with respect to one dimension. In both cases the exclusion statistics is a consequence of the no-double occupation constraint. We argue that the application of this formalism to hole-doped high Tc cuprates and the derived composite nature of the hole give a hint to grasp many unusual properties of these materials.