Density matrix renormalization group, 30 years on

The density matrix renormalization group (DMRG) algorithm pioneered by Steven White in 1992 is a variational optimization algorithm that physicists use to find the ground states of Hamiltonians of quantum many-body systems in low dimensions. But DMRG is more than a useful numerical method, it is a framework that brought together ideas from theoretical condensed matter physics and quantum information, enabling advances in other fields such as quantum chemistry and the study of dissipative systems. It also fostered the development and widespread use of tensor networks as mathematical representations of quantum many-body states, whose applications now go beyond quantum systems. Today, it is one of the most powerful and widely used methods for simulating strongly correlated quantum many-body systems. Six researchers discuss the early history of DMRG and the developments it spurred over the past three decades.