Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 24, 2004, Pages 1-12

  Dahnken, C ^a   Aichhorn, M ^b   Hanke, W ^a   Arrigoni, E ^b   Potthoff, M ^a  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; CLUSTER ANALYSIS; ENERGY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; SPECTRUM;

EID: 14944372418     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.245110     Document Type: Article

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43. This is due to the fact that, as in the expansion around the atomic limit of the Hubbard model, corrections beyond the CPT contain cumulants of higher-order correlation functions that vanish in the noninteracting limit (Ref. 5).
44. This approach has been recently suggested to introduce periodic boundary conditions. (Ref. 38). Hopping terms connecting the cluster boundaries are added to the Hamiltonian for the isolated cluster and then subtracted again within the CPT scheme. This procedure has turned out not to be satisfactory, however. Indeed it has been shown in Ref. 24 that open boundary conditions should be used for the variational CPT.
45. The physical self-energy is given by a stationary point of Ω[Σ]. This can be a minimum, maximum or a saddle point (Ref. 13). For a one-dimensional parameterization, Σ=Σ(h), there are minima and maxima in general. In case of several stationary points, the one with lowest Ω is stable thermodynamically. In case of a single parameter h this must be always at a minimum.
46. However, even in this case one should expect some reduction of the magnetization due to spin fluctuations with a wavelength shorter than the cluster size.