Spin Coherent Conductivity: Topological Protection of Spin Currents by Non-Commutative Plaquette Operators in OAM-Driven Quantum Spin Ladders

This repository contains the preprint, source code, and simulation data for the theoretical prediction of Spin Coherent Conductivity (SCC) — a new quantum transport phenomenon in which non-commutative plaquette operators provide topological protection of spin currents in orbital angular momentum (OAM) light-driven quantum spin systems. Key Results Introduction of the non-commutative plaquette operator Pₚlaq = Sxᵢ·Syⱼ·Sxₖ·Syₘ − Syᵢ·Sxⱼ·Syₖ·Sxₘ as a quantum vortex Hamiltonian — the spin-1/2 analogue of the Wilson loop in lattice gauge theory π-pulse OAM irradiation achieves 100. 4% spin current persistence (zero decay) at 300 K 2π-pulse achieves 129. 0% persistence (Spring-back amplification exceeding injected current) SCC effect scales with system size: +2. 7% (L=4) → +4. 7% (L=6) Temperature-independent topological protection (persistence increases with temperature) Experimentally testable prediction: OAM quantum number l switches material response between braking (l=1) and acceleration (l=2) via GCD (l, L) lattice matching Theoretical Framework This work is based on δ-theory, which classifies light–matter coupling into: PCC (Perturbative-Coupled Channel): one-way, separable input/response (e. g. , conventional laser → spin) SCC (Self-Consistent Channel): self-generated feedback where input and response are inseparable (e. g. , quantum vortex self-stabilization) The critical insight resolving the "bootstrap problem" of prior implementations: the non-commutative plaquette operator is the quantum vortex — not a measurement of it. Classical winding numbers yield zero in thermal states, but Pₚlaq detects quantum vortex correlations invisible to classical topology. Computational Method Simulations use the lambda3-memory-dft (DOI: 10. 5281/zenodo. 18228266) non-Markovian memory-augmented Schrödinger equation solver for exact diagonalization and Lanczos time evolution on spin-1/2 XY ladders with YBCO parameters (J = 130 meV) at finite temperature (Boltzmann-weighted thermal ensemble). Files Included sccₗetter. pdf — Preprint (3 pages, letter format) oamₓyₛimulatorᵥ3. py — Full simulation code (OAM-XY Simulator v3. 1, GPU-compatible, sparse matrix implementation for L≥8 systems) Relevance to Recent Publications This work connects to four concurrent publications (Feb–Mar 2026) converging on the paradigm of "designing quantum material properties through structural resonance": Nature (2026/2/25): Virtual photon control of superconductivity via hBN resonance (Basov et al. ) Advanced Materials (2026/3/4): Laser-written vortex structures for superconducting diode effect in α-Sn (Le Duc Anh, Tanaka et al. ) Communications Physics (2026/2/23): Paramagnon interference driving charge–spin cooperation in bilayer nickelates (Kontani et al. ) Nature Communications (2026/3/24): Nanofacet substrate engineering enhancing YBCO superconductivity by +15 K (Lombardi et al. ) OAM light uniquely encompasses all four approaches through its four control degrees of freedom (l, chirality, pulse length, wavelength), positioning it as a universal platform for quantum material design. Citation If you use this work, please cite: M. Iizumi "Spin Coherent Conductivity: Topological Protection of Spin Currents by Non-Commutative Plaquette Operators in OAM-Driven Quantum Spin Ladders, " Zenodo (2026).