Response functions in a one-dimensional Fermi gas and renormalization-group treatment of one-dimensional kondo lattices

E. Novais, E. Miranda, A. H. Castro Neto +1 more

We establish a mapping of a general spin-fermion system in one dimension into a classical generalized Coulomb gas. This mapping allows a renormalization-group treatment of the anisotropic Kondo chain both at and away from half-filling. We find that the phase diagram contains regions of paramagnetism, partial, and full ferromagnetic order. We also use the method to analyze the phases of the Ising-Kondo chain.

Guido Gentile, Vieri Mastropietro

E. Novais, E. Miranda, A. H. Castro Neto +1 more

We establish the phase diagram of the one-dimensional anisotropic Kondo lattice model at T = 0 using a generalized two-dimensional classical Coulomb gas description. We analyze the problem by means of a renormalization group treatment. We find that the phase diagram contains regions of paramagnetism, partial and full ferromagnetic order.

A. Langari, Vahid Karimipour

Jan Diekmann, Severin G. Jakobs

We investigate the functional renormalization group (FRG) flow of the two-particle vertex function of a model for x-ray absorption in metals. Concerning the appearance of logarithmic divergences, the model is prototypical for an important class of mostly zero- and one-dimensional systems which includes the Kondo model and the interacting one-dimensional Fermi gas. For our analysis, we formulate the FRG in the framework of the real-time zero-temperature formalism, in which the model was studied before with a parquet-based approach. We establish that a reasonably crafted, purely fermionic one-loop FRG approximation is fully equivalent on a detailed level to the leading-logarithmic parquet approximation. These two approximation schemes are thus found to just represent different perspectives on the same technical steps. This finding also reconfirms the traditional understanding of the capabilities of one-loop RG approximations for such models, which was recently put into question by an investigation of the x-ray-absorption model with multiloop FRG.

G. Benfatto, P. Falco, V. Mastropietro