Anomalous suppression of quantum chaos between two integrable limits

Level statistics in non-integrable quantum many-body systems with time reversal symmetry are expected to follow the Gaussian Orthogonal Ensemble (GOE), a hallmark of quantum chaos. However, we show that the interacting Su-Schrieffer-Heeger model exhibits a clear suppression of the mean level-spacing ratio $\langle r\rangle$ from the GOE value $\approx 0.535$, persisting deep in the nonintegrable regime. This challenges the conventional association between non-integrability and fully chaotic spectral statistics. Using exact diagonalization supported by semi-analytical arguments, we trace this anomaly to incomplete hybridization of many-body band states inherited from the noninteracting band structure. The resulting restructuring of the spectrum weakens level repulsion without restoring integrability. We show the robustness of this mechanism in extensions of the model which break chiral and inversion symmetry.