Renormalization-group study of Luttinger liquids with boundaries

We use Wilsons weak-coupling “momentum” shell renormalization-group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization-group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.

Figure 1

Topology of the second-order diagrams contributing to the RG flow.

Figure 2

Sketch of the trajectories of the weak-coupling RG flow in the ${{}_{\perp }\gamma }_1\text{−}{\gamma }_{1,2}$ plane $\left(X={{}_{\perp }\gamma }_1,Y={\gamma }_{1,2}\right)$. The dashed line indicates a line of stable fixed points. The fixed points on the dashed-dotted line are unstable.