Discord effects of inter-cluster interactions on a cluster-based Haldane state in a triangular spin tube

We have recently proposed a new concept of cluster-based Haldane states supported by an inherent chirality in a triangular spin tube with equivalent inter-cluster interactions. In this state, there appear spin-1/2 degrees of freedom consisting of a real spin and a scalar chirality as edge states. With applying a magnetic field, we can observe approximately a half of magnetization of S = 1/2 spin, i.e., a quarter spin magnetization, due to symmetrization of the real spin and the chirality. Here, we consider effects of discord between two types of inter-cluster interactions, inducing anisotropic biquadratic interactions of effective S = 1 spins. The discord brings the edge magnetization nearer to an exact value of quarter spin magnetization, whereas localization of the edge states becomes worse. These effects are also confirmed in a corresponding spin-1 model.