Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase

TL;DR

This paper maps the phase diagram of a spin-1 chain with a Haldane phase, revealing new phases and complex boundary features, with implications for Rydberg excitons in materials like Cu$_2$O.

Contribution

It provides an improved phase diagram of a spin-1 chain, identifying a new phase and triple points using advanced tensor-network computational methods.

Findings

Discovery of a new phase in the spin-1 chain.

Identification of triple points where phases meet.

Complex phase boundaries near the Haldane phase.

Abstract

We provide the phase diagram of a 2-parameter spin-1 chain that has a symmetry-protected topological (SPT) Haldane phase using computational algorithms along with tensor-network tools. We improve previous results, showing the existence of a new phase and new triple points. New striking features are the triple end of the Haldane phase and the complexity of phases bordering the Haldane phase in proximity allowing moving to nearby non-SPT phases via small perturbations. These characteristics make the system, which appears in Rydberg excitons, e.g. in Cu$_2$O, a prime candidate for applications.