Focus Series on Density Matrix Renormalization

Many interesting, novel and emergent phenomena in materials, such as fractional statistics, superconductivity, metal-insulator transitions and multiferroicity, are governed by electron correlations.

One of the most accurate and successful techniques able to tackle the complexity of these many-body correlated systems is the density-matrix renormalization group (DMRG), developed by Steve White in 1992 to study zero-temperature one-dimensional quantum models. Since then, it was extended to study models in higher dimensions, to calculate excited states, dynamical and time-dependent behavior, bosonic systems, complex molecules, and to include finite temperatures. It has also been extended to other fields in physics such as high energies, statistical physics, quantum information theory and as an efficient impurity-solver with the Dynamical Mean Field Theory (DMFT), one of the state-of-the-art methods to obtain electronic structure of correlated materials.

More recently, the development of similar techniques based on matrix product states led to the development of Tensor Network algorithms, including the Multi-scale Entanglement Renormalization Ansatz (MERA) for extending the method to quasi two-dimensional systems. Connections have also been established between the MERA method and conformal field theory.

This focus series on the "Density Matrix Renormalization" will bring together some important contributions using the DMRG, hoping it will: (i) give an idea to the general reader of the enormous usefulness and scope of this technique, and (ii) inspire the practitioner with new ideas to contribute to this constantly evolving field.