Thermodynamics of weakly coupled Falicov-Kimball chains from renormalization-group theory

TL;DR

This paper uses renormalization-group theory to analyze the thermodynamics of weakly coupled Falicov-Kimball chains, revealing how interchain hopping induces discontinuities in fermion occupation and addressing longstanding debates on phase transitions.

Contribution

It applies linear perturbation renormalization group to study thermodynamic properties of coupled Falicov-Kimball chains, highlighting the effects of weak interchain hopping on phase behavior.

Findings

Weak interchain hopping causes a discontinuity in fermion occupation.

The specific heat shows two maxima as a function of temperature.

The study addresses the controversy over discontinuous transitions in the model.

Abstract

The linear perturbation renormalization group is used to study spinless two-band fermion chains at half-filling. The model consists of two species of spinless fermions, namely localized f and extended p, and it takes into account the following: the kinetic energy of fermions p, the on-site Coulomb repulsion V between p and f fermions, chemical potentials {\mu}p and {\mu}f adjusted in such a way that the average of the site occupation = 1, and a weak interchain hopping tx . The average occupation number, the specific heat, and the correlation functions are studied as functions of temperature. For a single chain the occupation number is a smooth function of T and the specific heat displays two maxima. The weak interchain hopping triggers a discontinuity in the occupation number of fermions as a function of temperature. A long-standing controversy on whether the Falicov-Kimball model can describe a discontinuous transition of nf is also addressed.