Non-Hermitian J-Q model in the SU (2) limit: Sˣ channel reframing of Qc (δ) (v2)

Non-Hermitian J-Q model in the SU (2) limit: Sˣ channel reframing of Qc (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 Qc (δ) interpretation based on Sᶻ structure factor measurements. Subsequent analysis identified Sᶻ 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 The threshold interpretation in v1 is superseded and obsolete, not refined or extended, by this v2.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 Sᶻ-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 Sˣ 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 — HPHASESTABLE falsified with qualitative L-scaling asymmetry between hermitian and non-Hermitian limits. ** At Q=22, Sˣxᵤniform 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 Sˣxᵤniform (δ=1) /Sˣxᵤniform (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 Sˣxᵤniform 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 Sˣ 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.