Numerical evidences of spin-1/2 chain approaching spin-1 chain

TL;DR

This study uses numerical methods to show how a one-dimensional Heisenberg spin-1/2 alternating bond chain approaches the properties of a spin-1 chain, especially in the small AF to FM coupling ratio limit.

Contribution

It provides numerical evidence and analysis of the transition from a spin-1/2 alternating chain to a spin-1 chain, including edge states and gap comparisons.

Findings

Physical quantities match those of a spin-1 chain at small coupling ratio

Edge state behavior is analyzed in the small ratio limit

Haldane gap is four times larger in the spin-1 chain

Abstract

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.