The density-matrix renormalization group (DMRG) has shown to be one of the most reliable and versatile methods in modern computational physics. It can be applied to low-dimensional strongly correlated fermionic and bosonic systems and allow for a very precise calculation of static, dynamic and thermodynamic properties, especially in one dimension. Its field of applicability has now extended beyond Condensed Matter. It has been successfully used in Statistical Physics, Quantum Chemistry, Quantum Information, Nuclear and High Energy Physics.

     In recent years, there have been important improvements to this method. Some proposals to extend the method to two dimensions have been put forward by invoking the concept of quantum information. Significant advance has been achieved by generalizing the matrix-product representation of quantum states in one dimension to the tensor-product representation of quantum states or classical models in two dimensions.

     Due to the rapid progress in this field it is desirable for the community to gather every few years to discuss progress in this field. The previous two DMRG workshops were successfully held in Dresden (1998) and in Leiden (2004), respectively. This workshop will bring together once again the experts on DMRG to exchange new concepts and ideas, to foster conditions of communication and collaboration, and to attract junior research scientists and students to this fast growing field.