Asymptotic behaviour of large-scale solutions of Hitchin’s equations in higher rank

Abstract Let $X$ be a compact Riemann surface. Let $(E,\theta )$ be a stable Higgs bundle of degree $0$ on $X$ . Let $h_{\det (E)}$ denote a flat metric of the determinant bundle $\det (E)$ . For any $t\gt 0$ , there exists a unique harmonic metric $h_t$ of $(E,t\theta )$ such that $\det (h_t)=h_{\det (E)}$ . We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence $h_t$ is convergent to the naturally defined decoupled harmonic metric at the speed of the exponential order. We also obtain a uniform convergence for such a family of Higgs bundles.