Fig. 6: Convergence to analytical steady state of 1000-site noisy XXX Heisenberg chain.
From: Large-scale stochastic simulation of open quantum systems
a Time evolution of the local magnetization 〈Zj〉 for j = 1, …, 100 in an edge-driven XXX chain ( J = 1, h = 0), simulated using the TJM up to Jt = 100000 with timestep δt = 0.1 and boundary driving strength ϵ = 10π. Solid lines show the simulated trajectories, and dashed lines indicate the exact steady-state values \(\cos [\pi (\,j-1)/(L-1)]\). b Absolute deviation \({\Delta }_{{{{\rm{steady}}}}}=| \langle {Z}_{j}\rangle -{\langle {Z}_{j}\rangle }_{{{{\rm{ss}}}}}|\) on a logarithmic scale. The horizontal dashed line at 10−2 marks the target error, which is achieved by all sites by Jt ≈ 90000.
