Renormalization Group Potential for Quasi-One-Dimensional Correlated Systems

TL;DR

This paper develops a novel renormalization group framework for quasi-one-dimensional correlated systems using current-based interactions, revealing an RG potential that explains symmetry enhancements in ladder systems.

Contribution

It introduces a new formulation of RG equations as potential flows using current interactions, differing from traditional g-ology methods.

Findings

RG equations can be expressed as potential flows.

The RG potential explains symmetry enhancement in ladder systems.

Implications of the RG potential are discussed.

Abstract

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.