[Talk] Manuel Simonato – On the Spectral Properties of Inhomogeneous Luttinger Liquids

Speaker: Manuel Simonato

Title: On the spectral properties of inhomogeneous Luttinger liquids

Abstract: The physics of one-dimensional systems of interacting fermions strongly differs from the picture offeredby Fermi liquid theory. The low-energy properties of metallic, paramagnetic 1D Fermi systems arewell described by the Luttinger liquid (LL) theory. Among other properties, the homogeneous LL isknown to exhibit power-law behaviour for various correlation functions. For spin rotational invariantmodels, the exponents can be expressed in terms of a single parameterKρ, which is known to benon-universal.The LL concept emerged in the study of homogeneous systems with periodic boundary condition(PBC). In these models thelocal spectral functionshows a power-law suppression at energies asymp-totically close to the chemical potentialμ. Theoretically, this is very well understood and the exactLL parameterKρis known for a set of integrable models. In the last decades however, the interestshifted towards the investigation of LLs with PBC including impurities. The fact that these systemshave been shown to scale to chains with open ends led to the study of several models where openboundary condition (OBC) are introduced. As the translational invariance is broken, the exponent ofthe power-law suppression close to the boundary differs from the one in the bulk.The present work is devoted to the study of the local spectral function of two lattice models of LLswith open boundaries, namely the spinless fermions model with nearest neighbour interaction and the1D Hubbard model, with the methods of perturbation theory. It is demonstrated that many aspectsof the spectral properties can be understood within the HF theory. Despite what one usually readsabout one-dimensional interacting Fermi systems,in the presence of the boundaryperturbation theoryis already capable of providing meaningful results. Concurrently, this method also allows us to developan understanding of the dip appearing in the local spectral function at an energy different from thechemical potential.