One of the great challenges in condensed matter physics is the accurate simulation of strongly correlated systems. There have been many significant recent advances in this area. My talk will focus on tensor network methods (in particular the density matrix renormalization group (DMRG)), which have helped develop our understanding of quantum systems in low dimensions.  In addition to providing reliable numerical simulation tools, these methods have highlighted the importance of analysing reduced density matrices. In the first part of my talk I will present aspects of DMRG in the context of our work on randomly diluted antiferromagnets and the occurrence of anomalously scaling low energy "quasidegenerate states" (QD) at the percolation threshold [1, 2 ]. Motivated by this study, the second part of the talk will focus on the "quasidegenerate density matrix" (QDDM) [3], a mathematical construct involving diagonal and off-diagonal density matrices (those between all pairs of QD states). I will conclude by providing representative examples, in which numerical data from accurate many-body calculations was used to reveal the underlying order parameter and to detect a quantum phase transition.


[1] H.J. Changlani, S. Ghosh, S. Pujari, C.L. Henley, Phys. Rev. Lett. 111, 157201 (2013)
[2] L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006)
[3] C. L. Henley and H.J. Changlani, J. Stat. Mech. 2014(11), 11002 (2014)