Fragility of Symmetry Protected Topological Order on a Hubbard Ladder

TL;DR

This paper investigates the stability of the Haldane phase in a fermionic ladder, revealing its fragility under charge fluctuations and specific symmetries, which impacts the understanding of symmetry-protected topological phases.

Contribution

The study demonstrates how charge fluctuations can connect the Haldane phase to a trivial phase and identifies the reflection symmetries necessary for its stability.

Findings

Charge fluctuations can trivialize the Haldane phase.

Reflection symmetries are crucial for the phase's stability.

The Haldane phase is not robust against certain perturbations.

Abstract

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.