# Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states

## TL;DR

This paper explores the properties of integer spin antiferromagnetic chains, focusing on the Haldane gap and the edge states, revealing insights into their dependence on spin and the fragility of topological order.

## Contribution

It provides an analytical approximation for the Haldane gap at large spins and investigates the robustness of edge states using DMRG on spin ladders.

## Key findings

- Haldane gap scales with exchange coupling J
- Edge states' topological order diminishes smoothly with rung coupling
- Topological order in spin one chains is fragile and easily disrupted

## Abstract

The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappears smoothly by increasing the ladder rung coupling without any intervening phase transition. This is evidence for the fragile character of the topological order of the spin one chain.