Regensburg 2010 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 8: CE: (General) Theory
TT 8.8: Talk
Monday, March 22, 2010, 16:00–16:15, H21
Critical exponents and phase diagram of the Hubbard model — •Karsten Held1, Alessandro Toschi1, Georg Rohringer1, and Andrey Katanin2,3 — 1Institute of solid state physics, Vienna University of Technology — 2Max-Planck-Insitut für Festkörperphysik, Stuttgart — 3Institute of metal physics, Ekaterinburg
Despite being the prototype for strongly correlated electron systems, an accurate calculation of the critical behavior of the Hubbard model was hitherto not possible. With the recently developed dynamical vertex approximation (DΓA) [1], we are finally able to include non-local correlations beyond dynamical mean field theory (DMFT) in a systematic way - on all length scales. In two dimensions, this results in a reduction of the antiferromagnetic transition temperature to TN=0 [2], in agreement with the Mermin-Wagner theorem. In three dimensions, we get a non-mean-field critical behavior, in contrast to DMFT. It agrees, at least for half filling and large Coulomb repulsion, with the Heisenberg critical exponents.
By means of DΓA, we are also able to estimate the error of DMFT. In particular, we will discuss in which regions of the phase diagram a DMFT treatment is sufficient and where non-local correlations necessarily need to be included.
[1] A. Toschi, A. A. Katanin, K. Held, Phys. Rev. B 75, 045118 (2007).
[2] A. A. Katanin, A. Toschi, K. Held, Phys. Rev. B 80, 075104 (2009).