String order and adiabatic continuity of Haldane chains and band insulators

TL;DR

This paper demonstrates that the hidden string order characteristic of spin-1 Haldane chains also exists in one-dimensional band insulators and shows their adiabatic connection without phase transitions.

Contribution

It constructs Hamiltonians linking band insulators to topologically distinct spin models, revealing the persistence of string order in one dimension.

Findings

String order exists in 1D band insulators

Edge states in spin chains connect smoothly to surface states in insulators

String order is absent in higher dimensions

Abstract

The ground state of spin-1 Haldane chains is characterized by the so-called string order. We show that the same hidden order is also present in ordinary one-dimensional band insulators. We construct a family of Hamiltonians which connects adiabatically band insulators to two topologically non-equivalent spin models, the Haldane chain and the antiferromagnetic spin-1/2 ladder. We observe that the localized spin-1/2 edge-state characteristic of spin-1 chains is smoothly connected to a surface-bound state of band insulators and its emergence is not related to any bulk phase transition. Furthermore, we show that the string order is absent in any dimensions higher than one.