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We study the quantum fidelity (groundstate overlap) near quantum phasetransitions of the Ising universality class in one dimensional (1D) systems offinite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls,the anisotropic XY model), and in 1D topological insulators of anytopologically nontrivial Altland-Zirnbauer-Kitaev universality class. Therescaled fidelity susceptibility is a function of the only dimensionlessparameter LM, where 2M is the gap in the fermionic spectrum. We presentanalytic expressions for the fidelity susceptibility for periodic and openboundaries conditions with zero, one or two edgestates. The latter are shown tohave a crucial impact and alter the susceptibility both quantitatively andqualitatively. We support our analytical solutions with numerical data.

Universal fidelity near quantum and topological phase transitions in finite 1D systems