Semiclassical Approach to Competing Orders in Two-leg Spin Ladder with Ring-Exchange

TL;DR

This paper uses a semiclassical bosonic approach to analyze phase competition in a two-leg spin ladder with ring-exchange, revealing mutual induction phenomena between spin and chirality.

Contribution

It introduces a bosonic semiclassical framework that treats Nél and chirality orders equally, deriving effective actions for different phases and uncovering mutual induction effects.

Findings

Derived low-energy effective actions for phases

Revealed mutual induction between spin and chirality

Identified conditions for vector-chirality phase emergence

Abstract

We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hardcore bosons which treat the N\'eel and vector chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring-exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.