Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction

TL;DR

This paper explores the phase diagram of a spin-1/2 Heisenberg ladder with chirality interactions, revealing new phases and correlations, supported by analytical and numerical methods.

Contribution

It provides a comprehensive phase diagram including previously unexplored ferromagnetic and negative chirality interactions using bosonization and duality techniques.

Findings

Identifies multiple phases including rung singlet, Haldane, and non-magnetic ordered phases.

Shows phases with different dominant correlations such as spin, dimer, or chirality.

Numerical simulations confirm the analytical phase structure and critical properties.

Abstract

A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.