In this paper, we study the existence of solutions to the following Hartree equation

\begin{align*}\begin{cases}-\Delta u+\lambda V(x) u+\mu u=\left(\int_{\mathbb{R}^N}\frac{|u|^p}{|x-y|^{N-\alpha}}\right)|u|^{p-2}u,\ \text{in}\ \mathbb{R}^N,\\\int_{\mathbb{R}^N}|u|^2=\omega,\end{cases}\end{align*}

Where $N\geq 3$, $\omega,\lambda \gt 0$, $p\in \left(\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2}\right)\setminus\left\{\frac{N+\alpha+2}{N}\right\}$ and µ will appear as a Lagrange multiplier. We assume that $0\leq V\in L^{\infty}_{loc}(\mathbb{R}^N)$ has a bottom $int V^{-1}(0)$ composed of $\ell_0$ $(\ell_{0}\geq1)$ connected components $\{\Omega_i\}_{i=1}^{\ell_0}$, where $int V^{-1}(0)$ is the interior of the zero set $V^{-1}(0)=\{x\in\mathbb{R}^N| V(x)=0\}$ of V. It is worth pointing out that the penalization technique is no longer applicable to the local sublinear case $p\in \left(\frac{N+\alpha}{N},2\right)$. Therefore, we develop a new variational method in which the two deformation flows are established that reflect the properties of the potential. Moreover, we find a critical point without introducing a penalization term and give the existence result for $p\in \left(\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2}\right)\setminus\left\{\frac{N+\alpha+2}{N}\right\}$. When ω is fixed and satisfies $\omega^{\frac{-(p-1)}{-Np+N+\alpha+2}}$ sufficiently small, we construct a $\ell$-bump $(1\leq\ell\leq \ell_{0})$ positive normalization solution, which concentrates at $\ell$ prescribed components $\{\Omega_i\}^{\ell}_{i=1}$ for large λ. We also consider the asymptotic profile of the solutions as $\lambda\rightarrow\infty$ and $\omega^{\frac{-(p-1)}{-Np+N+\alpha+2}}\rightarrow 0$.