Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG)

This chapter is concerned with the problem of strongly correlated electrons in quantum chemistry. We describe how a technique known as the density matrix renormalization group (DMRG) can tackle complicated chemical problems of strong correlation by capturing the local nature of the correlations. We analyse the matrix product state structure of the DMRG wavefunction that encodes one-dimensional aspects of locality. We also discuss the connection to the traditional ideas of the renormalization group. We finish with a survey of applications of the DMRG, its strengths and weaknesses in chemical applications, and its recent promising generalization to tensor network states.