Regensburg 2013 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 51: Correlated Electrons: General Theory 1

TT 51.9: Talk

Thursday, March 14, 2013, 11:45–12:00, H6

Non-perturbative derivation of effective models using graph-based continuous unitary transformations — •Kris Cöster and Kai Phillip Schmidt — Lehrstuhl für Theoretische Physik I , TU Dortmund, 44221 Dortmund, Germany

Unitary transformations are an essential tool in many-body physics mapping the original model to a simpler effective model in a better suited basis. One way to schematically derive such unitary transformations is given by the so-called continuous unitary transformations (CUTs). For lattice models of finite dimension, these CUTs can be combined with graph theory to capture all zero-temperature fluctuations within a controlled spatial range (gCUTs) providing a robust non-perturbative scheme to derive effective low-energy models when at least one degree of freedom is gapped. This method has already been succesfully applied to various systems and the aim is to increase both the understanding and the accuracy of this novel tool. To this end we introduce a general recipe on each graph respecting all symmetries of the graphs. Furthermore, an intuitive truncation on each graph is gained. One particular challenge for gCUTs is that the graphs typically have less symmetries than the full lattice model. The impact of this reduced symmetry on the effective low-energy Hamiltonian is studied focussing on possible remedies. These aspects are tested for one-dimensional and two-dimensional quantum spin systems.