Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform

We study thermal transport along the edge of a small chiral-spin-liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs generates a thermal current that dynamically builds up and reaches a quasi-steady-state regime. In this time window, the two-terminal thermal conductance can approach half-quantized values -- a hallmark of Majorana-mediated transport -- under finely tuned conditions. The results agree with a steady-state Landauer-B\"uttiker description for sufficiently large reservoirs, where energy-resolved transmission rates help identify the optimal parameters to achieve the half-quantized conductance. This work provides a controllable platform to investigate topological thermal transport in engineered spin systems, such as realized in cold-atom and Rydberg-atom settings.