2014/07/16 by Christopher L. Henley, Hitesh J. Changlani · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2014/11/p11002
published as Journal of Statistical Mechanics: Theory and Experiment 2014 (11), P11002 · 24 pages, 5 figures, 1 table, submitted to JSTAT, Special Issue on "Quantum Entanglement in Condensed Matter Physics"
arxiv created 2014/07/16 · arxiv updated 2015/05/27
We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the "quasi-degenerate density matrix" (QDDM) which is rooted in Anderson's observation that the degenerate symmetry-broken states valid in the thermodynamic limit, are manifested in finite systems as a set of low-energy "quasi-degenerate" states (in addition to the ground state). This method, its original form due to Furukawa et al.[Phys. Rev. Lett. 96, 047211 (2006)], is given a number of improvements here, above all the extension from two-fold symmetry breaking to arbitrary cases. This is applied to two test cases (1) interacting spinless hardcore bosons on the triangular lattice and (2) a spin-1/2 antiferromagnetic system at the percolation threshold. In addition, we survey a different method called the "correlation density matrix", which detects (possibly long-range) correlations only from the ground state, but using the reduced density matrix from a cluster consisting of two spatially separated regions.