Non-Hermitian J-Q model in the SU(2) limit: S^x channel reframing of Q_c(δ) (v2)

Non-Hermitian J-Q model in the SU(2) limit: S^x channel reframing of Q_c(δ) (v2) Authors: Kamil Vargovský, Mária Vargovská Date: 15 May 2026 Supersedes: v1 (DOI 10.5281/zenodo.19451609, 7 April 2026) HPC allocation: Devana cluster, NSCC SAV, project p1927-26-t Changelog v1 → v2 Version 1 (April 2026) reported a threshold-monotonic Q_c(δ) interpretation based on S^z structure factor measurements. Subsequent analysis identified S^z as an inappropriate observable in the non-Hermitian (NH) regime due to broken rotational symmetry under δ ≠ 0. The threshold interpretation in v1 is superseded and obsolete, not refined or extended, by this v2. Quantitative v1 results remain valid as S^z-channel-specific observations within the measured range but should not be cited as universal phase-boundary characterization for the non-Hermitian J-Q model. Context The deconfined quantum critical point (DQCP) separating Néel antiferromagnetic and valence bond solid phases challenges the Landau-Ginzburg-Wilson framework. Zou et al. (arXiv:2511.03456, 2025) showed that NH perturbations weaken first-order tendencies at the DQCP in the easy-plane J-Q model (Δ=0.6). This work extends to the SU(2) limit (Δ=0) using sign-free SSE QMC on the square lattice with periodic boundary conditions. The S^x transverse channel is probed via an off-diagonal correlation estimator (Weber PhD §2.8 framework based), L ∈ {8, 12, 16, 24, 32, 48, 64}, δ ∈ [0, 1], Q ∈ [6, 40], T = 0.1. Full methodology reserved for follow-up publication. Key Findings Finding 1 — H_PHASE_STABLE falsified with qualitative L-scaling asymmetry between hermitian and non-Hermitian limits.** At Q=22, S^xx_uniform exhibits linear-in-(1/L) decay at δ=0 across L ∈ {16, 24, 32, 48, 64} (values 0.01112, 0.01013, 0.00964, 0.00859, 0.00806; L=48 anchor matches linear interpolation between L=32 and L=64 within 0.02σ), consistent with disordered-phase asymptotic scaling. At δ=1, the same L range shows monotonic growth with super-linear deviation from linear FSS (values 0.01170, 0.01131, 0.01125, 0.01307, 0.01556; the L=64 entry is the mean of 3 independent replica measurements at seeds {default, 2026051501, 2026051502}, SEM = 1.90×10⁻⁴, inter-replica scatter <2.1σ between any pair). The L=48 anchor at δ=1 lies 3.86σ below the linear-in-(1/L) interpolation between L=32 and L=64, confirming non-linear FSS deviation independent of L=64 single-measurement concerns. The L=64 ratio S^xx_uniform(δ=1)/S^xx_uniform(δ=0) = 1.931 ± 0.027 demonstrates 3-point L-scaling asymmetry (decay δ=0 vs accelerating growth δ=1) statistically robust at 20.2σ for δ=1 (L=32→L=64 transition) and 6.27σ for δ=0 (L=32→L=64 transition), independently established across 5 lattice sizes. Finding 2 — Sign-free preservation across 56 production configurations** spanning δ ∈ [0,1], Q ∈ [6,40], L ∈ [4,64]. Exact unity for ⟨sign⟩ and SignFracPos diagnostics confirms the analytical Marshall boundary |δ| ≤ 1 for the local per-bond decomposition. Finding 3 — No S^xx_uniform peak detected at δ ∈ {0.6, 1.0} within the measured Q range.** Monotonic decreasing behavior across Q ∈ [14, 40] at δ=0.6 and Q ∈ [6, 28] at δ=1.0. Different from the naïve Sandvik phase diagram [Sandvik 2007, arXiv:cond-mat/0611343] in the S^x channel within the measured Q range. Finding 4 — Interior minimum hypothesis for Q*(δ) crossover trajectory empirically falsified.** The L=24/L=16 ratio across an extended 6-point δ-scan yields a non-decreasing trajectory with a plateau between δ=0.3 and δ=0.5 within quoted precision. The interior minimum hypothesis, motivated by an initial 3-point δ-anchor (δ ∈ {0, 0.6, 1.0}), is empirically falsified by the 6-point measurement (δ ∈ {0, 0.3, 0.5, 0.6, 0.7, 1.0}). Interpretation (requires Phase 3) Whether the super-linear FSS deviation at δ=1 signals a phase transition crossover, the emergence of a distinct phase in the NH thermodynamic limit, or a Marshall local convention edge case, remains under investigation. The 3-replica statistical robustness at L=64 and L=48 anchor consistency reduce single-measurement concerns but do not resolve the underlying mechanism. Phase 3 outlook L=96 measurement for η extraction; dimer-dimer alternative order parameter cross-validation; sweep count scaling for calibration gap discrimination. Keywords: deconfined quantum criticality, non-Hermitian quantum mechanics, J-Q model, SSE QMC, finite-size scaling, sign-free Monte Carlo, SU(2) symmetry Subject areas: Condensed Matter Physics, Quantum Many-Body Systems, Computational Physics References 1. Zou, X., Yin, S., Li, Z.-X., Yao, H. "Unraveling Deconfined Quantum Criticality in Non-Hermitian Easy-Plane J-Q Model." arXiv:2511.03456 (2025). 2. Sandvik, A. W. "Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions." Phys. Rev. Lett. 98, 227202 (2007); arXiv:cond-mat/0611343. 3. Senthil, T. et al. "Deconfined quantum critical points." Science 303, 1490 (2004). 4. Weber, L. "Quantum Monte Carlo methods for critical quantum magnets." PhD thesis, RWTH Aachen University, 2022. This v2 supersedes the v1 (April 2026) interpretation. Full methodology, raw dataset, and production code are reserved for follow-up preprint publication. Technical correspondence on methodology and findings is welcome.