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TT: Fachverband Tiefe Temperaturen

TT 28: CE: (General) Theory 2

TT 28.2: Talk

Tuesday, March 15, 2011, 14:15–14:30, HSZ 105

Phase diagram and criticality of the three dimensional Hubbard model in the Dynamical Vertex Approximation — •Georg Rohringer¹, Alessandro Toschi¹, Andrey Katanin², and Karsten Held¹ — ¹Institute for Solid State Physics, Vienna University of Technology, Austria — ²Institute of Metal Physics, Ekaterinburg, Russia

Inclusion of spatial correlations on all length scales beyond the dynamical mean field theory (DMFT) induces two relevant changes to the phase-diagram of the three dimensional Hubbard model: i) a sizable reduction of the Néel temperature (T_N) for the onset of antiferromagnetic long-range order; (ii) a deviation from then mean-field critical behavior for T ∼ T_N. Both effects are well captured by means of the recently developed[1] Dynamical Vertex Approximation (DΓA) applied to the half-filled Hubbard model: We find[2] a reduction of the Néel temperature of ∼ 30 %, which agrees with previous cluster calculations in the intermediate-to-strong coupling regime. Furthermore we observe a temperature region of deviation from the mean field criticality, which increases with the interaction strength U. Remarkably, the critical exponents extracted for the highest U values well agree with those of the three-dimensional Heisenberg universality class. Finally, DΓA also allows for a quantitative estimation of the errors stemming from the purely local nature of DMFT, when it is applied to a (realistic) finite dimensional case.
A. Toschi, A. Katanin, K. Held, Phys. Rev. B 75, 045118 (2007) & Phys. Rev. B 80, 075104 (2009).
G. Rohringer, A. Toschi, A. Katanin, K. Held in preparation.