Density matrix renormalization group (DMRG)

DMRG is a method for computing expectation values of various quantities at the ground state of a given Hamiltonian that describes a quantum many-body system in discrete space. It can be viewed as a variational method using the matrix product state (MPS) as a variational wave function. Therefore, it provides a precise approximation in the cases where the matrix product state is a good description of the target state. One-dimensional systems is a typical example. The precision of the approximation can be controlled by the dimension of the tensor indices (the bond dimension). The quality of the result can therefore be evaluated by altering the bond dimension. Since the MPS is a special case of the tensor network state (TNP), DMRG can be regarded as one of the tensor network methods.