Density-matrix based numerical methods for discovering order and correlations in interacting systems

摘要

We review recently introduced numerical methods for the unbiased detection ofthe order parameter and/or dominant correlations, in many-body interactingsystems, by using reduced density matrices. Most of the paper is devoted to the"quasi-degenerate density matrix" (QDDM) which is rooted in Anderson'sobservation that the degenerate symmetry-broken states valid in thethermodynamic limit, are manifested in finite systems as a set of low-energy"quasi-degenerate" states (in addition to the ground state). This method, itsoriginal form due to Furukawa et al.[Phys. Rev. Lett. 96, 047211 (2006)], isgiven a number of improvements here, above all the extension from two-foldsymmetry breaking to arbitrary cases. This is applied to two test cases (1)interacting spinless hardcore bosons on the triangular lattice and (2) aspin-1/2 antiferromagnetic system at the percolation threshold. In addition, wesurvey a different method called the "correlation density matrix", whichdetects (possibly long-range) correlations only from the ground state, butusing the reduced density matrix from a cluster consisting of two spatiallyseparated regions.