Valence bond solid states with symplectic symmetry

TL;DR

This paper introduces a one-dimensional valence bond solid state with symplectic symmetry SP(n), constructs its Hamiltonian, and demonstrates properties like a spectral gap, exponential decay of correlations, and string order, akin to Haldane's conjecture.

Contribution

It presents a novel SP(n) symmetric VBS state, constructs its parent Hamiltonian, and analyzes its physical properties, extending the understanding of quantum antiferromagnets.

Findings

The VBS state has a spectral gap.

Correlation functions decay exponentially.

The state exhibits string order.

Abstract

We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry SP(n) and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.