Non-perturbative aspects of currents in one-dimensional systems of strongly correlated systems

Sam T. Carr

Thierry Giamarchi

Alexei M. Tsvelik

In these Lectures we discuss some aspects of theory of strongly correlated low-dimensional systems. In (1+1) and two dimensions availability of non-perturbative techniques makes it possible to obtain solutions of non-trivial models. One of such techniques is called bosonization. In this course we discuss a generalization of this technique for systems with isotopic symmetry.

Hiroyuki Shiba, Masao Ogata

There are two fundamental models for one-dimensional strongly correlated electrons: the Hubbard model and the t-J model. Recent intensive efforts have led to clarifying many important aspects of those systems, whose low-energy behaviors can be described as Luttinger liquid. This paper reviews current status of our understanding, which has been achieved with analytic and numerical approaches.

Fabian H. L. Eßler

Ming-Shyang Chang, Wei Chen, Hsiu‐Hau Lin

We studied the correlated quasi-one-dimensional systems by one-loop renormalization group techniques in weak coupling. In contrast to conventional g-ology approach, we formulate the theory in terms of bilinear currents and obtain all possible interaction vertices. Furthermore, the one-loop renormalization group equations are derived by operator product expansions of these currents at short length scale. It is rather remarkable that these coupled non-linear equations, after appropriate rescaling, can be casted into potential flows. The existence of what we nicknamed “RG potential ” provides a natural explanation of the emergent symmetry enhancement in ladder systems. Further implications arisen from the RG potential are also discussed at the end. Quasi-one-dimensional (Q1D) systems have attracted extensive attentions from both experimental and theoretical aspects. 1),2) Due to the low dimensionality, strong quantum fluctuations often give rise to surprising behaviors, which are rather different from our intuitions built in higher dimensions. It is then exciting to explore