Berlin 2012 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 10: Correlated Electrons: (General) Theory 1

TT 10.1: Talk

Monday, March 26, 2012, 15:00–15:15, H 3010

Enhanced Perturbative Continuous Unitary Transformation — •Holger Krull, Nils A. Drescher, and Götz S. Uhrig — TU Dortmund, Theoretical Physics I, 44221 Dortmund, Germany

We present an enhanced version of continuous unitary transformations (CUTs) to derive effective models perturbatively and non-perturbatively for quantum lattice models. The underlying idea is to expand the Hamiltonian and the generator of the flow equation in the expansion parameter. The operators are described in second quantization. For the method to be efficient, it is essential to keep track of the relevant contributions according to their order in the expansion parameter. This enhanced perturbative CUT (epCUT) allows us to determine effective Hamiltonians to high order. In contrast to perturbative CUT, the expansion around unperturbed Hamiltonians with non-equidistant spectrum is possible. In addition, we found that the set of differential flow equations of the epCUT can be integrated non-perturbatively leading to a robust extrapolation similar to self-consistent diagrammatic techniques. This directly evaluated epCUT (deepCUT) provides robust results even for relatively large expansion parameter as long as the relevant processes with a spatial range up to the correlation length are included. The epCUT and the deepCUT are illustrated for the S=1/2 antiferromagnetic Heisenberg ladder and for an extension with alternating rung couplings implying a non-equidistant unperturbed spectrum. The results for the ground state energy (order 17/16) and the dispersion (order 15/13) are presented.