The density matrix renormalization group method (DMRG) is a powerful numerical method for strongly correlated systems, which often cannot be solved analytically either by the mean field approach or through perturbation. The DMRG is originally proposed as an iterative search of the ground state in one dimension. With more researchers involving in the development of the algorithms based on DMRG, now it has become an optimized unbiased method for the strongly correlated problems. Compared with other numerical methods, the DMRG has one drawback that it cannot handle the lattices in three dimension. However, many materials with layered structure like the high-Tc superconductors can be approximated by the two dimensional lattice, and some models can be simplified or transformed into lower dimensions without losing information under certain situations. Here we have studied models of the electron systems in one dimension, and the spin systems in two dimension with large scale DMRG. For the Kondo lattice model we have found two charge-ordered phases in the doped regime which have not been found before. We also investigate the spin-12 XY model on the honeycomb lattice and identify a chiral spin liquid with additional chiral interactions. The chiral spin liquid has a non-trivial topological order with chiral edge states. Regarding the twisted bilayer graphene which is found experimentally to emerge a superconducting phase at low temperature, we construct an auxiliary model and provide insights to the exotic ferromagnetic Mott state that may exists in the twisted bilayer graphene. We also try to study the Kondo impurity problem in the presence of a superconductor and discuss the potential models with realistic interactions for future studies.