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The fidelity is widely used to detect quantum phase transition, which ischaracterized by either a sharp change of fidelity or the divergence offidelity susceptibility in the thermodynamical limit when the phase-drivingparameter is across the transition point. In this work, we unveil that theoccurrence of exact zero of fidelity in finite-size systems can be applied todetect quantum phase transitions. In general, the fidelity$\mathcal{F}(\gamma,\tilde{\gamma})$ always approaches zero in thethermodynamical limit, due to the Anderson orthogonality catastrophe, no matterwhether the parameters of two ground states ($\gamma$ and $\tilde{\gamma}$) arein the same phase or different phases, and this makes it difficult todistinguish whether an exact zero of fidelity exists by finite-size analysis.To overcome the influence of orthogonality catastrophe, we study finite-sizesystems with twist boundary conditions, which can be introduced by applying amagnetic flux, and demonstrate that exact zero of fidelity can be alwaysaccessed by tuning the magnetic flux when $\gamma$ and $\tilde{\gamma}$ belongto different phases. On the other hand, no exact zero of fidelity can beobserved if $\gamma$ and $\tilde{\gamma}$ are in the same phase. We demonstratethe applicability of our theoretical scheme by studying concrete examples,including the Su-Schrieffer-Heeger model, Creutz model and Haldane model. Ourwork provides a practicable way to detect quantum phase transition via thecalculation of fidelity of finite-size systems.

Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions