Dresden 2009 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 6: Postersession Correlated Electrons: (General) Theory, Low-Dimensional Systems, Kondo Physics, Heavy Fermions, Quantum-Critical Phenomena
TT 6.5: Poster
Montag, 23. März 2009, 13:00–16:45, P1A
Matrix product state calculation of the correlation density matrix: an unbiased analysis of long-range correlations — •Wolfgang Münder1, Andreas Weichselbaum1, Jan von Delft1, and Christopher Henley2 — 1Department of Physics and Center for NanoScience, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilans-Universität, Theresienstrasse 37, 80333 Munich — 2LASSP, Clark Hall, Cornell University, Ithaca, NY 14853-2501
A useful concept for determining the dominant correlations of the ground state wave function of a lattice model, in an unbiased fashion without prior knowledge, is the correlation density matrix (CDM) [1]. For two disjoint, separated clusters A and B, it is defined to be the density matrix of their union, minus the direct product of their respective density matrices, ρABCDM = ρA ∪ B − ρA ⊗ ρB. It encodes all possible correlations between the clusters A and B and has block-diagonal form, dictated by the symmetries of the Hamiltonian. We analyse it for a family of interacting spinless fermion models on a ladder [1], which has nontrivial mappings to free fermions in certain limits [2]. We use the density matrix renormalization group (implementing Abelian symmetries explicitly) to calculate the ground state in the form of a matrix product state, from which the correlation density matrix can straightforwardly be obtained. We also discuss methods for extracting the Luttinger liquid scaling exponents from the correlation density matrix.
[1] S.-A. Cheong and C.L. Henley, arXiv:0809.0075v1 (2008).
[2] S.-A. Cheong, PhD thesis, Cornell Univ., (2007), http://people.ccmr.cornell.edu/~clh/Theses/cheong-habis.pdf