Renormalization group study of interacting fermions at finite temperatures

C. Bourbonnais, Benoit Guay, Rachel Wortis

Hiroshi Takano, Masaru Onoda, Ikuo Ichinose +1 more

Fabio Siringo, G. G. N. Angilella, R. Pucci

A renormalization-group (RG) analysis of the superconductive instability of an anisotropic fermionic system is developed at a finite temperature. The method appears as a natural generalization of Shankar's approach to interacting fermions and of Weinberg's discussion about anisotropic superconductors at T=0. The need of such an extension is fully justified by the effectiveness of the RG at the critical point. Moreover the relationship between the RG and a mean-field approach is clarified, and a scale-invariant gap equation is discussed at a renormalization level in terms of the eigenfunctions of the interaction potential, regarded as the kernel of an integral operator on the Fermi surface. At the critical point, the gap function is expressed by a single eigenfunction and no symmetry mixing is allowed. As an illustration of the method we discuss an anisotropic tight-binding model for some classes of high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors, exhibiting a layered structure. Some indications on the nature of the pairing interaction emerge from a comparison of the model predictions with the experimental data. \textcopyright{} 1996 The American Physical Society.

Dražen Zanchi, Heinz J. Schulz

We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this method to the Hubbard model on a square lattice using both zero- and finite- temperature methods. Truncating the effective action at the sixth term in fermionic variables we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability Tc^{RG} as function of doping. We calculate furthermore the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type d while the AF fluctuations are of the type s Following the strength of both SC and AF fluctuation along the instability line we obtain the phase diagram. The temperature Tc^{RG} can be identified with the crossover temperature T{co} found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime Tc^{RG} corresponds to the superconducting critical temperature.

R. Shankar

Julian Lichtenstein, David Sánchez de la Peña, D. Rohe +3 more