Winding numbers of phase transition points for one-dimensional topological systems

Abstract

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.

5 pages, 5 figures

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• Topological analysis of the complex SSH model using the quantum geometric tensor
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• Scattering description of edge states in Aharonov-Bohm triangle chains
• Charge waves and dynamical signatures of topological phases in Su-Schrieffer-Heeger chains
• Proximity-induced flat bands and topological properties in a decorated diamond chain
• Entanglement entropy as a probe of topological phase transitions