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r in a specific channel. Also to be mentioned here is the increased efficiency of the calculations of two-particle Green's functions of the AIM in continuous-time quantum Monte Carlo (Ref);
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Such a choice for the standard deviation of the DOS (0.5) for the cubic lattice makes our DMFT results comparable with the corresponding ones for a square lattice with t = 0.25 and a Bethe lattice of semibandwidth W / 2 = 1.
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This can be easily seen by the following argument: Consider a diagram that is reducible in one of the two particle-hole channels as that shown in Fig. It is evident that the subdiagram A can be separated from B by cutting the Green's function lines a and b. Let us assume that the diagram is reducible in the (1 4)-(2 3) channel as well, i.e., it can be split into two parts, one containing the outer legs 1 and 4 the other one containing 2 and 3 by cutting two internal lines. This would be only possible if the subdiagrams A and B could be split into two parts by cutting only one internal line. But, this is impossible since it would lead to subdiagrams with three outer legs, which violates particle conservation. Therefore, it is proven that each diagram is either fully irreducible or reducible in exactly one channel.
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To the best of our knowledge, an analytic expression of F for the atomic limit has been derived by in the Appendix of Ref. Our independent derivation essentially confirms this result, except for some minor corrections.
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m contains diagrams reducible in the transverse ph channel and, due to the SU(2) and the crossing symmetries, they coincide with the corresponding magnetic ones.
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