  Fidelity approach has been widely used to detect various types of quantum
phase transitions, including some that are beyond the Landau symmetry breaking
theory, in condensed matter models. However, challenges remain in locating the
transition points with precision in several models with unconventional phases
such as the quantum spin liquid phase in spin-1 Kitaev-Heisenberg model. In
this work, we propose a novel approach, which we named the fidelity map, to
detect quantum phase transitions with higher accuracy and sensitivity as
compared to the conventional fidelity measures. Our scheme extends the fidelity
concept from a single dimension quantity to a multi-dimensional quantity, and
use a meta-heuristic algorithm to search for the critical points that globally
maximized the fidelity within each phase. We test the scheme in three
interacting condensed matter models, namely the spin-1 Kitaev Heisenberg model
which consists of the quantum spin liquid phase and the topological Haldane
phase, the spin-1/2 XXZ model which possesses a Berezinskii-Kosterlitz-Thouless
transition, and the Su-Schrieffer-Heeger model that exhibits a topological
quantum phase transition. The result shows that the fidelity map can capture a
wide range of phase transitions accurately, thus providing a new tool to study
phase transitions in unseen models without prior knowledge of the system's
symmetry.
