  In this paper, we establish a $p$-adic Simpson correspondence on the arena of
Liu-Zhu for rigid analytic varieties $X$ over $\Cp$ with a liftable good
reduction by constructing a new period sheaf on $X_{\proet}$. To do so, we use
the theory of cotangent complex after Beilinson and Bhatt. Then we give an
integral decompletion theorem and complete the proof by local calculations. Our
construction is compatible with the previous works of Faltings and Liu-Zhu.
