Quasi-fractionalization of spin in a cluster-based Haldane state supported by chirality of a triangular spin tube

Fractionalization of quantum degrees of freedom holds the key to finding new phenomena in physics, e.g., the quark model in hadron physics, the spin-charge separation in strongly-correlated electron systems, and the fractional quantum Hall effect. A typical example of the fractionalization in quantum spin systems is the spin-$1$ Haldane state, whose intriguing characteristics are well described by fractionalized $S=1/2$ virtual spins in a bilinear-biquadratic spin-$1$ chain, the so-called Affleck--Kennedy--Lieb--Tasaki model, delivering two individual spin-$1/2$ degrees of freedom as edge states. Here we theoretically propose an exotic extension of the Haldane state and chirality in a triangular spin tube, inducing a quasi-fractionalization of spin-$1/2$ degree of freedom, i.e., a quarter spin. Existence of the edge state is confirmed both analytically and numerically, combining a low-energy perturbation theory and variational matrix-product state method. Our study can not only propose a new quantum spin property but pave a way to novel quantum states of matter.