Berlin 2015 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantenmechanik I

MP 9.1: Vortrag

Mittwoch, 18. März 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.