Quantum spin Hall effect protected by spin U(1) quasisymmetry

Quantum spin Hall (QSH) insulators, with their unique helical edge states where counterpropagating edge channels possess opposite spins, have attracted broad interest across various fields. While the exact quantization of spin Hall conductance (SHC) is elusive in realistic materials due to intrinsic spin mixing effects, the near quantization, as a compromised definition of the QSH effect, cannot be captured by rigorous topological invariants. In this Letter, we present a universal symmetry indicator for diagnosing the QSH effect in realistic materials, termed spin U(1) quasisymmetry. Such a symmetry eliminates the first-order spin-mixing perturbation and thus protects the near-quantization of SHC, applicable to time-reversal-preserved cases with either ${Z}_{2}=1$ or ${Z}_{2}=0$, as well as time-reversal-broken scenarios. We propose that spin U(1) quasisymmetry is hidden in the subspace spanned by the doublets with unquenched orbital momentum and emerges when SOC is present, which can be realized in 19 crystallographic point groups. Our theory is applied to identify previously overlooked QSH phases such as time-reversal-preserved even spin Chern phase and time-reversal-broken phase, as exemplified by twisted bilayer transition metal dichalcogenides, monolayer ${\mathrm{RuBr}}_{3}$, and monolayer FeSe. Our work provides a comprehensive symmetry-based framework for understanding the QSH effect and significantly expands the material pool for the screening of exemplary material candidates.