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

TL;DR

This paper proposes a new quantum spin state in a triangular spin tube that exhibits quasi-fractionalization of spin, supported by analytical and numerical evidence, expanding the understanding of fractionalized quantum states.

Contribution

It introduces an exotic extension of the Haldane state with chirality, demonstrating quasi-fractionalization of spin-1/2 in a triangular spin tube, supported by theoretical and numerical methods.

Findings

Existence of edge states confirmed analytically and numerically.

Demonstration of quasi-fractionalization of spin-1/2 as a quarter spin.

Proposal of a new quantum spin property and state of matter.

Abstract

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.