7 son Model can be reduced to the Hubbard Model if we replace the Green’s function of the conduction electrons of PAM subsystem by tunneling Green’s function of hop- ping electrons of HM. This equivalence is irrelevant for the kinetic properties of PAM. It is important to emphasize that there is a close simi- larity between our results obtained for two different mod- els of strongly correlated systems such as Periodic Ander- son Model (PAM) and the Hubbard Model (HM). From comparison of the results obtained for the PAM (see pa- per [17]) and the results of the present paper for the HM the topological coincidence of the diagrams for both models has been revealed. For example the skeleton diagrams of Fig. 3 of paper [17], obtained for Λ functional of PAM topologically co- incide with the skeleton diagrams of our Fig. 2 for the same functional, but of quite a different model. In or- der to obtain a complete coincidence, it is necessary to replace the full Green’s function G$_{c}$ ( iω ) of conduction electrons of PAM by the renormalized tunneling Green’s function T ( iω ) of the HM. The same similarity exists between other functionals of these models. For example, comparison of the skele- ton diagrams of Fig. 10 of paper [17] with the diagrams of Fig. 4 of the present paper reveals the full coinci- dence upon replacement of the Green’s functions G$_{c}$ by T . This comparison allows us to conclude that from the thermodynamic point of view the Periodic Ander- Two of us (V.A.M. and L.A.D.) thank Professor N.M. Plakida and Doctor. S. Cojocaru for fruitful discussion. We also note that the skeleton representation of our functional allows to select the local irreducible Green’s functions as can be seen from Figs. 2 and 10. These quantities contain only fluctuations in time, unlike the non local ones which include both fluctuations in time and space. The coefficients of local diagrams (see Fig. 10) vary with the order of perturbation theory as 1 2 n$_{−}$ $^{1}$n ! for n > 1. Only such local diagrams are relevant for DMFT, so that one can attempt to carry out the summation of this class of diagrams. Acknowledgments ∗ Electronic address: mosckalen@theor.jinr.ru 21 J. M. Luttinger, Phys. Rev. 119 , 1153 (1960). 20 J. M. Luttinger and J. C. Ward, Phys. Rev. 118 , 1417 (1960). 19 A. Georges, G. Kotliar, W. Krauth and M. J. Rozenberg, Rev. Mod. Phys. 8 , 13 (1996); G. Kotliar and D. Vollhardt, Physics Today 57 , 53 (2004). 18 V. A. Moskalenko, L. A. Dohotaru and R. Citro, Diagrammatic theory for Periodic Anderson Model: Stationary property of the thermodynamic potential, arXiv:1001.1644v1[cond-mat.str-el], (2010). 17 V. A. Moskalenko, P. Entel, L. A. Dohotaru and R. Citro, Teor. Mat. Fiz. 159 , 500 (2009); [Theor. Math. Phys. 159 , 454 (2009)]. 16 V. A. Moskalenko, P. Entel, L. A. Dohotaru, D. F. Digor and R. Citro, Diagrammatic theory for Anderson Impurity Model, Preprint BLTP, JINR, Dubna, E17-2008-56. 15 V. A. Moskalenko, P. Entel, D. F. Digor, L. A. Dohotaru and R. Citro, Teor. Mat. Fiz. 155 , 914 (2008); [Theor. Math. Phys. 155 , 535 (2008)]. 14 V. A. Moskalenko, P. Entel, and D. F. Digor, Phys. Rev. B59 , 619 (1999). 13 V. A. Moskalenko, Teor. Mat. Fiz. 116 , 456 (1998);[ Theor. Math. Phys. 116 , 1094 (1998)]. 12 V. A. Moskalenko, Teor. Mat. Fiz. 110 , 308 (1997);[ Theor. Math. Phys. 110 , 243 (1997)]. 10 N. N. Bogoliubov and V. A. Moskalenko, Teor. Mat. Fiz. 86 , 16 (1991);[ Theor. Math. Phys. 86 , 10 (1991)]; Doklady AN SSSR 316 , 1107 (1991); JINR Rapid Communications 44 , 5 (1990). 9 S. I. Vakaru, M. I. Vladimir and V. A. Moskalenko, Teor. Mat. Fiz. 85 , 248 (1990);[ Theor. Math. Phys. 85 , 1185 (1990)]. 8 M. I. Vladimir and V. A. Moskalenko, Teor. Mat. Fiz. 82 , 428 (1990); [Theor. Math. Phys. 82 , 301 (1990)]. 7 A. A. Abrikosov, L.P.Gor’kov and I. E. Dzyaloshinsky, The method of quantum field theory in statistical physics, Do- brosvet, Moscow (1998). 6 N. N. Bogolyubov, Full Collection of Papers, Vol.10, Nauka, Moscow (2007). 11 N. N. Bogoliubov and V. A. Moskalenko, Teor. Mat. Fiz. 92 , 182 (1992); [Theor. Math. Phys. 92 , 820 (1992)]; 5 J. Hubbard, Proc. Roy. Soc. A285 , 542 (1965). 4 J. Hubbard, Proc. Roy. Soc. A281 , 401 (1964). 3 J. Hubbard, Proc. Roy. Soc. A276 , 238 (1963). 2 V. A. Moskalenko, L. A. Dohotaru and I. D. Ceb- otari, Diagrammatic analysis of the Hubbard model: Stationary property of the thermodynamic potential, arXiv:1001.1647v1[cond-mat.str-el], (2010). 1