Non-Hermitian Stabilization of Antiferromagnetic Order in the SU(2) J-Q Model: A Sign-Free SSE QMC Study of Q_c(δ)

The deconfined quantum critical point (DQCP) separating Néel antiferromagnetic (AFM) and valence bond solid (VBS) phases represents one of the central open problems in quantum magnetism, challenging the Landau-Ginzburg-Wilson paradigm. Zou et al. (arXiv:2511.03456, 2025) demonstrated that non-Hermitian (NH) perturbations weaken first-order tendencies at the DQCP in the easy-plane J-Q model (Δ=0.6). We extend this study to the SU(2) limit (Δ=0) using sign-free Stochastic Series Expansion (SSE) Quantum Monte Carlo on the square lattice (L=24, 32), performed on Devana HPC (NSCC SAV, project p1927-26-t). The NH perturbation H_nH shifts the critical coupling Q_c in a nonlinear, threshold manner. Below δ≈0.3, Q_c remains at its Hermitian value (≈22, consistent with Sandvik 2007). Above the threshold, stabilization of the AFM phase becomes dramatic: Q_c > 48 at δ=0.6 (lower bound shift +118%) and Q_c > 80 at δ=1.0 (lower bound shift +264%). The threshold δ* lies in the interval (0.3, 0.6). This behavior is consistent with the NH operator transitioning from RG-irrelevant to RG-relevant above δ*. The sign-free condition for |δ|≤1 follows from Marshall rotation on the bipartite lattice, yielding non-negative weights (1±δ)/2. Verified analytically and numerically: ⟨sign⟩ = 1.000 across all simulation points. These results extend Zou et al. into the SU(2) limit and provide the first systematic Q_c(δ) curve in this regime. Physical interpretation in terms of complex RG fixed points remains open. Extraction of the anomalous dimension η(δ) at the corrected Q_c(δ) is reserved for follow-up work.This preprint establishes priority for the results presented. Full methodology and extended data will be published in a follow-up manuscript.