Interacting fermions in one dimension: from weak to strong correlation

This talk reviews some recent progresses in the studies of low dimensional electronic models of strong correlations.

In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.

Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics ...

In this perspective we discuss recent theoretical and experimental concepts giving a route to a better understanding of conventional and unconventional pairing mechanisms between opposite-spin fermions arising in one-dimensional mesoscopic systems. With special attention, we focus on the problem of experimental detectability of correlations between particles. We argue that state-of-the-art experiments with few ultracold fermions may finally break an impasse and give pioneerin...

This is a reprint volume devoted to exact solutions of models of strongly correlated electrons in one spatial dimension by means of the Bethe Ansatz.

Table of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization group for interacting fermions 5. Single impurity in a 1D system: scattering theory for interacting electrons 6. Bosonization solution 7. Transport in quantum wires 7.1 Conductivity and conductance 7.2 Dissipation in a contactless measurement 7.3 Conductance of a wire attached to...

In these notes I review the basic concepts of the effects of interactions on quantum particles. I focuss here mostly on the case of fermions, but several aspects of interacting bosons are mentioned as well. These notes have been voluntarily kept at an elementary level and should be suitable for students wanting to enter this field. I review the concept of Fermi liquid, and then move to a description of the interaction effects, as well as the main models that are used to tackl...

We present explicit expressions for the correlation functions of interacting fermions in one dimension which are valid for arbitrary system sizes and temperatures. The result applies to a number of very different strongly correlated systems, including mesoscopic quantum wires, quantum Hall edges, spin chains and quasi-one-dimensional metals. It is for example possible to calculate Coulomb blockade oscillations from our expression and determine their dependence on interaction ...

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary conf...