Density matrix of disjoint regions as a way of determining dominant correlations in interacting systems

In the context of strongly correlated systems, studying the ground state reduced density matrix (or derived quantities, such as the entanglement entropy and spectrum) of a local region has turned out to be useful for characterizing a wide variety of phases. However, to make definitive quantitative mappings of lattice simulations to field theories one needs to go beyond the density matrix of a single region. We use critical spin chains to demonstrate how information from the density matrix of disjoint regions (obtained from the density matrix renormalization group) [1,2] can be used to calculate the low-lying scaling dimensions (and operators) of the corresponding conformal field theory. In a related context, we will also discuss the use of density matrices that involve more than just the ground state, as a way of detecting order in the system [3]. [1] W. Muender, A. Weichselbaum, A. Holzner, J. von Delft, C. L. Henley, New. J. Phys., 12, 075027 (2010) [2] H.J. Changlani, O. Sule, S. Ryu (in preparation) [3] C. L. Henley and H.J. Changlani, J. Stat. Mech. 2014(11), 11002 (2014)