To mitigate this issue, local correlation theories that exploit sparsity have been proposed. One type of these methods is based on pair domain constructions as long distance between orbital centroids leads to weakly interacting electron pairs and therefore little energy contribution. This approach facilitates the construction of pair domains, enabling the MP2 residual equations or CCSD equations to be solved with linear scaling. Examples of methods based on pair domain construction include Cluster-in-Molecule (CIM), Local MP2, CCSD, and CCSD(T) (L-MP2/CCSD/CCSD(T)), as well as the widely used Domain-Based Local Pair Natural Orbital methods (DLPNO-MP2/CCSD/CCSD(T)). There are also works on how CCSD(T) solver could be embedded in a DFT calculation, i.e., WFT in DFT embedding. Density Matrix Embedding Theory (DMET) represents another local correlation approach, re-lying on partitioning the system into multiple domains or 'fragments'. However, unlike methods that use occupied molecular orbital pairs to construct local domains, DMET partitions the system into fragments and relates the all-electron (molecular) Hamiltonian to the fragment Hamiltonian via an orbital transformation matrix. The energies are typically obtained from the oneand two-particle density matrices (1-and 2-PDM) of the fragments, though novel approaches based on constructing expectation values from a fragment-recovered 'wavefunction' have been proposed. Various advancements related to DMET have been made, including enhancing the robustness of the correlation potential fitting via semidefinite programming (SDP), implementations in periodic systems, studies on superconductivity and other properties in strongly correlated systems, analytical gradient theory, and stochastic implementations. The objective of this work is to accelerate the post-HF calculation process in self-consistent DMET by leveraging the decay in the orbital transformation matrix and the mean-field 1-PDM.