Deformation of anisotropic Fermi surfaces due to electron - electron interactions

– We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface. Introduction. – An open question in the study of the interactions in anisotropic metallic systems is the deformation of the Fermi surface induced by the interactions. The Fermi surface is one of the key features needed to understand the physical properties of a material. Recent improvements in experimental resolution have led to high precision measurements of the Fermi surface (FS), and also to the determination of the many-body effects in the spectral function, as reported by ARPES experiments [1]. The interpretation of experiments in anisotropic strongly correlated systems remains a complex task [2]. The FS depends on the self-energy corrections to the quasiparticle energies, which, in turn, depend on the shape of the Fermi surface. Hence, there is an interplay between the self-energy corrections and the FS topology. For weak local interactions, the leading corrections to the FS arise from second order diagrams. The self energy, within this approximation, can show a significant momentum dependence when the initial FS is anisotropic and lies near hot spots (see below). This simultaneous calculation of the FS and the second order self energy corrections is a formidable task. Many approaches have been used to study this problem like pertubation theory [3], bosonization methods [4, 5], or perturbative Renormalization Group calculations [6–8], and the cellular dynamical mean-field theory (CDMFT), an extension of Dynamical Mean Field Theory [9]. In this work, we calculate perturbation theory corrections and use Renormalization Group arguments [10, 11] in order to study analytically the qualitative corrections to the shape of the FS induced by the electron-electron interaction. This method allows us to classify the different features of the FS from the dependence of the self-energy corrections on the value of