Anfuso and Rosch [Phys. Rev. B 75, 144420 (2007)] showed that the “topological” Haldane phase in a fermionic spin-$1/2$ ladder can be continuously deformed into a “trivial” phase without explicitly breaking symmetries when local charge fluctuations are taken into account. Within the framework of symmetry-protected topological phases, we revisit the model and demonstrate how the Haldane phase can be adiabatically connected to a trivial phase due to charge fluctuations. Furthermore, we show that the Haldane phase remains stable as long as the system is symmetric under particular reflection symmetries.

• Received 15 January 2015

DOI:https://doi.org/10.1103/PhysRevB.91.155128