Let $\rho$ be a Hitchin representation for PSL(n,R) and f be the unique $\rho$-equivariant harmonic map from the universal cover of the hyperbolic surface to the corresponding symmetric space. We show its energy density is at least 1 and the rigidity holds. In particular, we show given a Hitchin representation, every equivariant minimal immersion from a hyperbolic plane into the corresponding symmetric space is distance-increasing. Moreover, the equality holds at one point only if it holds everywhere and $\rho$ is an n-Fuchsian representation.