# Ground state properties of the bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain

## TL;DR

This study investigates the ground state properties, excitation spectra, and order parameters of a bond alternating spin-1/2 anisotropic Heisenberg chain, revealing the presence of a Haldane phase with coexisting dimer and string orders.

## Contribution

It provides analytical and numerical analysis of the ground state, dispersion, and spin gap in bond alternating chains, highlighting the emergence of the Haldane phase in anisotropic conditions.

## Key findings

- Spin gap appears with bond non-uniformity in AFM-AFM chain.
- Dimer and string orders coexist in the ground state.
- Haldane phase persists across most anisotropic regions.

## Abstract

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.