Two-dimensional algorithm of the density-matrix renormalization group

We propose an approach to implement the density-matrix renormalization group (DMRG) in two dimensions. With this approach the initial blocks of a $L\times L$ lattice are built up directly from the matrix elements of a $\left(L-1\right)\times \left(L-1\right)$ lattice and the topological characteristics of two-dimensional lattices are preserved in the iteration of DMRG. By applying it to the spin-1/2 Heisenberg model on both square and triangular lattices, we find that this approach is significantly more efficient and accurate than other two-dimensional DMRG methods currently in use.