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

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.