Understanding heavy fermion from generalized statistics

TL;DR

This paper explores how incomplete statistics can model the distribution of heavy electrons in superconducting materials, providing a new theoretical framework that links the statistics parameter q to the coupling constant J in the Kondo model.

Contribution

It introduces the application of incomplete statistics to describe heavy electron behavior, connecting the parameter q to the coupling J, offering a novel theoretical perspective.

Findings

Heavy electrons can be modeled with incomplete statistics.

The parameter q correlates with the coupling constant J.

This approach explains the Fermi surface flattening effect.

Abstract

Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi-Dirac statistics and non-standard theories such as fractional exclusion statistics for anyons and Tsallis nonextensive statistics. The present work is an attempt to account for the heavy electron distribution within incomplete statistics (IS) which is developed for complex systems with interactions which make the statistics incomplete such that sum_i p_i^q=1. The parameter q, when different from unity, characterizes the incompleteness of the statistics. It is shown that the correlated electrons can be described with the help of IS with q related to the coupling constant J in the context of Kondo model