Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets

TL;DR

This paper reviews the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, explores its persistence in quasi-one-dimensional systems, and provides numerical evidence of its topological nature and phase diagram.

Contribution

It offers a comprehensive numerical analysis of the phase diagram and confirms the Haldane phase as a symmetry protected topological state in quasi-one-dimensional geometries.

Findings

Haldane phase persists in quasi-1D geometries.

Phase diagram mapped for realistic models.

Haldane phase confirmed as a symmetry protected topological state.

Abstract

We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Haldane phase of spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the quasi-one-dimensional Haldane phase is indeed a non-trivial symmetry protected topological state.