Quasiparticle dispersion of the 2D Hubbard model: From an insulator to a metal.

On the basis of Quantum-Monte-Carlo results the evolution of the spectral weight A(k, ω) of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features: a quasiparticle-like dispersive narrow band of width of the order of the exchange interaction J and a broad valence-and conduction-band background. The continuous evolution is traced back to one and the same many-body origin: the doping-dependent antiferromagnetic spin-spin correlation. 1 Recent results of angle resolved photoemission spectroscopy (" ARPES ") [1] revealed strong similarities in the low-energy excitations of a prototype insulating copper oxide, i.e. Sr 2 CuO 2 Cl 2 [2], and metallic cuprates like Bi 2212, Bi 2201, etc.: in both cases the quasiparticle (QP) band has rather small dispersion of typically 1 eV width, it is separated from a broad main valence-band " background " (of about 6 eV width) in much the same way, the k-dispersion is similar and also the intensity modulation as function of energy is comparable. Thus, it appears that the dispersive metallic band evolves continuously from the insulating limit and has a similar physical origin as the undoped valence band in the cuprates. This has important consequences for the copper oxides: the excitation spectrum in the insulating case is decisively determined by many-body effects, documented by the known difficulties of one-electron bandstructure calculations for the insulating limit [1], which then strongly emphasizes a many-body origin of the QP dispersion also in the metallic case. In this work Quantum-Monte-Carlo (QMC) results for the angular resolved photoemis-sion spectral weight A(k, ω) for the two-dimensional (2-D) Hubbard model are reported which demonstrate for this " generic " model the above strong similarities between undoped insulating and doped metallic situations: in particular, we find in both cases a very similar small dispersive low-energy band, for which the band width is set by the exchange interaction J ∼ 4t 2 /U when the Coulomb correlation U is of order of the non-interacting bandwidth 8t. This new feature is shown in the metallic case to be essentially unrenormalized (for electronically filled, i.e. ω < µ states) from the insulating band, while above the chemical potential µ additional states with again an energy scale set by J are filled in. A(k, ω) is inferred from the QMC data by applying Bayesian probability theory in the frame of " …