The study of entanglement in many-body systems has led to a deeper understanding of quantum phase transitions and the performance of numerical algorithms such as the density matrix renormalization group (DMRG). Understanding the structure of state space and particular states such as ground and thermal states is one of the major topics in the quantum information theoretical assessment of many-body systems. As their complexity scales exponentially in the number of particles, it is important to identify subsets in state space that are well suited to describe a certain system and allow for an efficient description. One branch within this line of research is concerned with so called entanglement area laws, which has shown that the entanglement content of typical states occurring in nature is much lower than generic states. A review may be found here:

• J. Eisert, M. Cramer and M.B. Plenio. Area laws for quantum and classical correlations. Rev. Mod. Phys. 82, 277 – 306 (2010)

We also work on the development and implementation of DMRG–and its time-dependent version tDMRG–methods, and use them to address problems drawn from an extremely broad range of topics in physics, biology and chemistry. The breadth of our DMRG and t-DMRG work is strongly driven by our recent development of a DMRG/tDMRG method which accurately simulates the dynamics and ground states of a huge class of open quantum systems. With this tool we are currently investigating dissipation, decoherence and irreversibility in many-body systems and important theoretical models such as the spin-boson model.

• J. Prior, A.W. Chin, S.F. Huelga and M.B. Plenio. Efficient simulation of strong system-environment interactions. Phys. Rev. Lett. 105, 050404 (2010)
• A.W. Chin, A. Rivas, S.F. Huelga and M.B. Plenio. Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials. J. Math. Phys. 51, 092109 (2010)
• M.P. Woods, M. Groux, A.W. Chin, S.F. Huelga and M.B. Plenio. Mappings of open quantum systems onto chain representations and Markovian embeddings. E-print arXiv:1111.5262 [quant-ph]