A toy model for localized to itinerant electron transitions

TL;DR

This paper introduces a simplified statistical model to simulate the transition of electrons from localized to itinerant states, capturing key features of phase changes like the cerium $ taeta$ transition.

Contribution

It presents a novel toy model that mimics localized-to-itinerant electron transitions, providing insights into phase crossover phenomena in correlated electron systems.

Findings

Identifies a specific interaction energy parameter $J$ where the crossover occurs.

Shows a transfer of charge carriers from itinerant to localized states.

Provides a crude analogy to the cerium $ taeta$ transition.

Abstract

A toy statistical model which mimics localized-to-itinerant electron transitions is introduced. We consider a system of two types of charge carriers: (1) localized ones, and (2) itinerant ones. There is chemical equilibrium between these two. The solution of the model shows that there is a crossover, at a specific value of a local interaction energy parameter $J$, at which carriers transfer from being itinerant to a localized/mixed valence state. The model has a very crude analogy to the observed $\gamma\rta\alpha$ transition in metal cerium.