Quasi-fractionalization of edge spin in chirality-assisted cluster-based Haldane state on triangular spin tube

Abstract

Fractionalization of quantum degrees of freedom holds the key to finding new phenomena in physics, e.g., the quark model in hadron physics and the spin-charge separation in strongly-correlated electron systems. A typical example of the fractionalization in quantum spin systems is the spin-1 Haldane state, whose intriguing characteristics are well described by fractionalized virtual spins, delivering two individual spin-1/2 degrees of freedom as edge states. Here we theoretically propose an exotic extension of the Haldane state to the pseudo spin-1 model consisting of the mixture of real spin and spin chirality, resulting in quasi-fractionalization of spin-1/2 magnetization, i.e., an approximately-1/4 spin. Existence of the edge state is confirmed both analytically and numerically in a triangular spin tube, combining a low-energy perturbation theory and variational matrix-product state method. Our study not only proposes an unconventional quantum spin object but paves a way to chop the elementary quantities further.