Natural extension of hidden $Z_2 \times Z_2$ symmetry toward arbitrary integer spin chains

TL;DR

This paper extends the understanding of hidden $Z_2 imes Z_2$ symmetry in integer spin chains, showing how entangled valence-bond states are disentangled via the Kennedy-Tasaki transformation, revealing boundary states and symmetry properties.

Contribution

It generalizes the hidden symmetry analysis from spin-1 to arbitrary integer spins, providing explicit expressions and boundary state characterizations.

Findings

Disentanglement of valence-bond states by Kennedy-Tasaki transformation.

Identification of boundary Ising-like states with $Z_2$ variables.

Explicit spin decomposition and boundary matrix expressions.

Abstract

We show how entangled valence-bond singlet pairs are disentangled partially and totally by the Kennedy-Tasaki transformation which reveals the hidden $Z_2\times Z_2$ symmetry in valence-bond-solid chains as a higher-spin generalization of the previous studies toward the intermediate-$D$ state. The totally disentangled states correspond to four Ising-like states with $Z_2$ variables on the boundary. We present a simple expression of results by using the spin decomposition and the boundary matrix.