Symmetry-resolved Rényi fidelities and quantum phase transitions

We introduce a family of quantum R\'enyi fidelities and discuss their symmetry resolution. express the symmetry-resolved as Fourier transforms charged fidelities, for which we derive exact formulas fermionic Gaussian states. These results also yield formula total states, expect to have applications beyond scope this paper. investigate in XX spin chain focus on (i) between thermal states (ii) reduced density matrices at zero temperature. Both can detect phase transition chain. Moreover, argue that are sensitive inner structure In particular, they through reorganization charge sectors critical point. This main feature be general. highlight transitions thermodynamic limit.