Abstract
An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.
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Jarrell, M., Pruschke, T. Magnetic and dynamic properties of the Hubbard model in infinite dimensions. Z. Physik B - Condensed Matter 90, 187–194 (1993). https://doi.org/10.1007/BF02198153
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DOI: https://doi.org/10.1007/BF02198153