q-deformations of quantum spin chains with exact valence-bond ground states

TL;DR

This paper explores q-deformations of quantum spin chains with exact valence-bond ground states, generalizing known models and introducing new anisotropic variants, including a novel spin-1/2 Majumdar-Ghosh model.

Contribution

It applies q-deformation techniques to construct generalized quantum spin chain models with exact valence-bond ground states, including a new anisotropic spin-1/2 Majumdar-Ghosh model.

Findings

Recovered the anisotropic spin-1 VBS model

Developed a new anisotropic spin-1/2 Majumdar-Ghosh model

Demonstrated the applicability of q-deformation to spin chain models

Abstract

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighbouring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-1/2 Majumdar-Ghosh model.