Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange

TL;DR

This paper investigates the phase transitions in an S=1/2 spin ladder with four-spin ring exchange using perturbative and bosonization methods, revealing a second-order transition and a gapped, dimerized phase.

Contribution

It provides a comprehensive analysis of the phase diagram of the spin ladder with ring exchange, combining strong and weak coupling approaches to identify transition points and critical behavior.

Findings

Large ring exchange induces a second-order phase transition.

Critical exponent for the gap is approximately 1.

High ring exchange leads to a gapped, dimerized phase.

Abstract

The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\eta\simeq1$, in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase emerging for high values of the ring exchange is argued to be gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.