Non-Hermitian Stabilization of Antiferromagnetic Order in the SU (2) J-Q Model: A Sign-Free SSE QMC Study of Qc (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 HₙH shifts the critical coupling Qc in a nonlinear, threshold manner. Below δ≈0. 3, Qc remains at its Hermitian value (≈22, consistent with Sandvik 2007). Above the threshold, stabilization of the AFM phase becomes dramatic: Qc > 48 at δ=0. 6 (lower bound shift +118%) and Qc > 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 Qc (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 Qc (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.