Related papers: Physics in one dimension: theoretical concepts for…
In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum…
The concept of a Luttinger liquid has recently been established as a fundamental paradigm vital to our understanding of the properties of one-dimensional quantum systems, leading to a number of theoretical breakthroughs. Now theoretical…
One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a…
We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids.…
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…
Gapless many-body quantum systems in one spatial dimension are universally described by the Luttinger liquid effective theory at low energies. Essentially, only two parameters enter the effective low-energy description, namely the speed of…
This chapter reviews the theoretical description of interacting fermions in one dimension. The Luttinger liquid concept is elucidated using the Tomonaga-Luttinger model as well as integrable lattice models. Weakly coupled chains and…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the…
The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and…
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from…
Interacting fermion systems in one dimension, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional exchange statistics. This is shown…
A selfconsistent many body approach for the description of gases with quartets, trions, and pairs is presented. Applications to 3D Fermi systems at low density are discussed.
The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions, in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum…
The concept of a Tomonaga-Luttinger liquid (TLL) has been established as a fundamental theory for the understanding of one-dimensional quantum systems. Originally formulated as a replacement for Landau's Fermi-liquid theory, which…
Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum…
Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been…
Microscopically probing quantum many-body systems by resolving their constituent particles is essential for understanding quantum matter. In most physical systems, distinguishing individual particles, such as electrons in solids, or…
The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in…
I attempt to give a pedagogical overview of the progress which has occurred during the past decade in the description of one-dimensional correlated fermions. Fermi liquid theory based on a quasi-particle picture, breaks down in one…