We introduce a scheme for constructing order parameters (OPs) in translationally invariant systems by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by nonlocal invariants, we demonstrate that our real-space OPs provide a more refined classification. In the extended Su-Schrieffer-Heeger model, we show that the standard winding number is insufficient to fully distinguish all phases; our OPs reveal a hidden substructure where each topological sector splits into two distinct phases. Beyond identifying the phase boundaries, these OPs quantify the depth of a phase, and remain robust in characterizing transitions in disordered systems. Furthermore, our approach provides a practical finite-size diagnostic for the Berezinskii-Kosterlitz-Thouless transition in the interacting spin-$\frac{1}{2}$ XXZ model. The presented framework offers a broadly applicable tool for uncovering the phase diagrams of diverse interacting and noninteracting quantum many-body systems.

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• BKT transition
• Order parameters
• Quantum phase transitions
• Topological phases of matter
• Su-Schrieffer-Heeger model
• XYZ model