Abstract

Ground states of integer spin chains are known since the late 80’s to sustain highly non local order described by infinite string operators of the spins. Such states defy the usual Landau theory description and can be considered simple prototypes of topological order. Recently we established the existence of an analogous phase of spinless bosons, which exhibits similar string order in terms of the boson density. Moreover, the Bose system can be tuned across quantum phase transitions between the exotic phase, which we term Haldane insulator, and the conventional Mott and density wave states. The response of the system to external perturbations near these phase transitions is revealing of the unusual character of the string order. In particular I will show how a perturbation, seemingly unrelated by symmetry to either phase, eliminates the critical point between the Mott and Haldane phases and allows adiabatic connection between them. Finally I will establish the existence of a distinct collective mode that can serve to identify the new phase in Bragg spectroscopy experiments.