Berlin 2015 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 9: Quantenmechanik I
MP 9.1: Talk
Wednesday, March 18, 2015, 11:45–12:05, HFT-FT 101
Transfer matrices and excitations with matrix product states — •Valentin Zauner1, Damian Draxler1, Laurens Vanderstraeten2, Matthias Degroote2, Jutho Haegeman2, Marek M Rams3, Vid Stojevic4, Norbert Schuch5, and Frank Verstraete1 — 1University of Vienna, Vienna, Austria — 2University of Ghent, Ghent, Belgium — 3Krakow University of Technology, Krakow, Poland — 4University College London, London, UK — 5RWTH Aachen, Aachen, Germany
We investigate the relation between static correlations in the ground state of local many-body Hamiltonians and the low energy dispersion relations using the formalism of tensor network states. We show that the Matrix Product State Transfer Matrix (MPS-TM) – a central object in the computation of static correlation functions – provides important information about the location and magnitude of the minima of the low energy dispersion and present numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models. We elaborate on the peculiar structure of the MPS-TM’s eigenspectrum and give several arguments for the close relation between the structure of the low energy spectrum of the system and the form of static correlation functions. Finally, we discuss how the MPS-TM connects to the exact Quantum Transfer Matrix. We also present a renormalization group argument which allows to reinterpret variational MPS techniques (such as the Density Matrix Renormalization Group) as an application of Wilson’s Numerical Renormalization Group along the virtual (imaginary time) dimension of the system.