C080 - The system evolves under the Lindblad master equation d rho/dt = -(i/hbar)[H_s,rho] + sum...
Verdict: verified
Location: Supp. Mat. S6, Eqs. (S11-S13)
Type / expected artifact: math / math
Claim: The system evolves under the Lindblad master equation d rho/dt = -(i/hbar)[H_s,rho] + sum_j DL_j with DL_j = L_j rho L_j^dag - (1/2){L_j^dag L_j, rho}, and the singlet fidelity follows F(t) ~= 1 - C_0 e^{-R_t t}, R_t being the Liouvillian gap.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain verified -> verified.
Source location(s): source/supp_content.tex:183-196 (Eqs. (S11-S13)).
Conclusion
Lindblad/GKSL master equation + dissipator form confirmed (paper's Eq S12 'L_k' in anticommutator is a typo for L_j). qutip Liouvillian at (1.95J,2.58J,0.29pi,beta=J): exactly one zero eigenvalue (unique steady state), steady-state singlet fidelity = 1.000000, gap = 0.11424 J. mesolve from |dd> + tail fit 1-F=C0 exp(-Rt) gives R_fit=0.11424 J = gap exactly (ratio 1.0000). So F(t)~1-C0 e^{-R_t t} with R_t the Liouvillian gap is confirmed. Conclusion: verified.
Verification details
Derivation excerpt: The claimed evolution is the standard Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation $$ \dot\rho = -\frac{i}{\hbar}[H_s,\rho] + \sum_{j=1}^{4}\mathcal DL_j, \qquad \mathcal DL_j = L_j\rho L_j^{\dagger} - \tfrac12\{L_j^{\dagger}L_j,\rho\}. $$ (The paper's Eq. S12 writes $L_k$ inside the anticommutator, which is a typo for $L_j$; the dissipator is the usual diagonal GKSL form, trace-preserving and completely positive.) Here $H_s$ is Eq. S9 (C078) and $\{L_j\}$ are the four jump operators (C079). This is exactly qutip.liouvillian(H_s, c_ops).
Executable rerun: run.py exited 0 in 1.112s; log verification/C080/attempts/R002/run.log.
Output excerpt:
top 6 eigenvalue real parts: [-0. -0.11424 -0.39887 -0.39887 -0.39887 -0.39887]
number of ~zero eigenvalues (steady states): 1
Liouvillian gap (|slowest nonzero Re|): 0.11424 J
steady-state singlet fidelity: 1.000000
fitted F(t) tail rate R_fit = 0.11424 J (C0=1.0793)
ratio gap/R_fit = 1.0000
final fidelity F(t=200) = 1.00000