We prove the convergence of the Sasamoto-Spohn model in equilibrium to the energy solution of the stochastic Burgers equation on the whole line. The proof, which relies on the second order Boltzmann-Gibbs principle, follows the approach of  and does not use any spectral gap argument.
"Scaling of the Sasamoto-Spohn model in equilibrium." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/18-ECP206