Unveiling quantum phase transitions by fidelity mapping

Fidelity has been widely used to detect various types of quantum phase transitions (QPTs). However, challenges remain in locating the transition points with precision in several models with unconventional phases. We propose the fidelity map approach to detect QPTs with higher accuracy and sensitivity than the conventional fidelity measures. Our scheme extends the fidelity concept from a single-dimensional to a multidimensional quantity and uses a metaheuristic algorithm to search for the critical points that globally maximize the fidelity within each phase. We verify the scheme in several interacting models that possess unconventional phases and QPTs, namely, the spin-1 Kitaev-Heisenberg model, the spin-1/2 XXZ model, and the interacting Su-Schrieffer-Heeger model. The fidelity map can capture a wide range of phase transitions accurately even in small systems, thus providing a convenient tool to study QPTs in unseen models without prior knowledge of the symmetry of the system.