Novel Approach to Unveil Quantum Phase Transitions Using Fidelity Map

The study of quantum phases and quantum phase transitions (QPTs) has been one of the most active research areas in condensed matter physics. Identifying quantum phase transitions is key to understanding complex and novel properties in condensed matter such as unconventional superconductors and topological materials. Fidelity has been widely used to detect various types of QPTs in interacting many-body systems. However, several unconventional transitions remain difficult to identify with current methods. We propose a novel approach, i.e. the fidelity map, to detect QPTs with higher accuracy and sensitivity as compared to the conventional fidelity measures. Our scheme extends the fidelity concept from a single-dimensional to a multi-dimensional quantity and uses a meta-heuristic algorithm to search for the critical points that globally maximize the fidelity within each phase. The resulting "fidelity map" can capture a wide range of phase transitions accurately even in small and novel systems without prior knowledge, expanding the available toolset to study phase transitions in new quantum many-body systems.