Identifying whether a many-body ground state is gapped or gapless is a fundamental yet challenging problem, especially in quantum spin liquids. In this work, we develop a gap-diagnostic scheme based on the polarization amplitude defined via twist operator, evaluated within the infinite density-matrix renormalization group framework. As a benchmark, an analysis of the spin-$\frac{1}{2}$ XXZ chain demonstrates that the polarization amplitude clearly distinguishes the gapless Tomonaga-Luttinger liquid from the gapped Néel phase. We then extend this framework to infinite cylinders of the spin-$\frac{1}{2}$ XY-$J_{\chi }$ model on the square lattice. We find that the polarization amplitude sharply detects the transition between the gapless XY phase and the gapped chiral spin liquid phase. These results show that polarization amplitudes provide a strong energy gap diagnostic in two-dimensional frustrated quantum magnets, including quantum spin liquids.

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• Order parameters
• Quantum phase transitions
• Quantum spin liquid
• 1-dimensional spin chains
• Antiferromagnets
• Mott insulators
• Quantum many-body systems
• Heisenberg model
• Hubbard model
• Tensor network methods
• XY model