Speakers: Karsten Held (Institute for Solid State Physics, TU Wien)
Place: Na Slovance, main lecture room
Presented in English
Organisers:
Department of Condensed Matter Theory
Abstract
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,
in agreement with the Mermin-Wagner theorem. In three dimensions,
we get a non-mean-field critical behavior, in contrast to DMFT.
It approximately 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. Besides, DΓA is also promising to apply to
nanoscopic
systems [2].
[1] A. Toschi, A. A. Katanin, K. Held, Phys. Rev. B 75, 045118
(2007); Phys. Rev. B 80, 075104 (2009).
[2] A. Valli et al., Phys. Rev. Lett. 104, 246402 (2010).
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