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Fidelity approach has been widely used to detect various types of quantumphase transitions, including some that are beyond the Landau symmetry breakingtheory, in condensed matter models. However, challenges remain in locating thetransition points with precision in several models with unconventional phasessuch as the quantum spin liquid phase in spin-1 Kitaev-Heisenberg model. Inthis work, we propose a novel approach, which we named the fidelity map, todetect quantum phase transitions with higher accuracy and sensitivity ascompared to the conventional fidelity measures. Our scheme extends the fidelityconcept from a single dimension quantity to a multi-dimensional quantity, anduse a meta-heuristic algorithm to search for the critical points that globallymaximized the fidelity within each phase. We test the scheme in threeinteracting condensed matter models, namely the spin-1 Kitaev Heisenberg modelwhich consists of the quantum spin liquid phase and the topological Haldanephase, the spin-1/2 XXZ model which possesses a Berezinskii-Kosterlitz-Thoulesstransition, and the Su-Schrieffer-Heeger model that exhibits a topologicalquantum phase transition. The result shows that the fidelity map can capture awide range of phase transitions accurately, thus providing a new tool to studyphase transitions in unseen models without prior knowledge of the system'ssymmetry.

Novel Approach to Unveil Quantum Phase Transitions Using Fidelity Map