Anomalous low-doping phase of the Hubbard model

Abstract

We present results of a systematic Quantum-Monte-Carlo study for the single-band Hubbard model. Thereby we evaluated single-particle spectra (PES & IPES), two-particle spectra (spin & density correlation functions), and the dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow to identify different physical regimes. Near half-filling we find an anomalous 'Hubbard-I phase', where the band structure is, up to some minor modifications, consistent with the Hubbard-I predictions. At lower temperatures, where the spin response becomes sharp, additional dispersionless 'bands' emerge due to the dressing of electrons/holes with spin excitatons. We present a simple phenomenological fit which reproduces the band structure of the insulator quantitatively. The Fermi surface volume in the low doping phase, as derived from the single-particle spectral function, is not consistent with the Luttinger theorem, but qualitatively in agreement with the predictions of the Hubbard-I approximation. The anomalous phase extends up to a hole concentration of ≈ 15%, i.e. the underdoped region in the phase diagram of high-Tc superconductors. We also investigate the nature of the magnetic ordering transition in the single particle spectra. We show that the transition to an SDWlike band structure is not accomplished by the formation of any resolvable 'precursor bands', but rather by a (spectroscopically invisible) band of spin 3/2 quasiparticles. We discuss implications for the 'remnant Fermi surface' in insulating cuprate compounds and the shadow bands in the doped materials.71.10. Hf,71.10.Fd,75.40.Gb

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

“…11 the spectral function A k (ω) for U = 8 along high-symmetry directions in the Brillouin zone of the chemical lattice. The result is compared with the result from the usual CPT (h = 0) and with numerically exact QMC data from Gröber et al 37 which are available for an N c = 8 × 8 isolated cluster and finite but low temperature (T = 0.1). The spectral function A k (ω) obtained from the maximum-entropy method (see Ref.…”

“…From previous QMC studies 37 it is well known that the quasi-particle band is the dispersion of a spin bag, i.e. an additional hole (electron) which is dressed by the local distortions of the spin order that are produced by the motion of the hole in the antiferromagnetic background.…”

Calculation of Density of States for FeAs-based Superconductors

“…Nevertheless, we can try to analyze the doped situation, assuming the normal filling of the zone by charge carriers while maintaining the calculated spectral density (the so-called "hardzone" approximation). This description of strongly correlated systems is not entirely correct, but considering the fact that the profile of the Fermi surface, as shown by our results, is weakly dependent on the interaction parameter, near the half-filling it is possible to obtain data that can carry useful information, for example, about the features of the Fermi-liquid (or not) behavior of carriers [18]. We assume that near the Fermi surface the distortion of the zones by changing the carrier concentration n at constant U is weaker than by changing of U with a constant density n.…”

Electron spectral density of the half-filled Hubbard model in the atomic limit at finite temperature

“…A non-perturbative quantum Monte Carlo (QMC) method provides possibility to compare electronic properties of the Hubbard model at t ½ U obtained in the Hubbard-I approximation to the QMC numerical results. Such comparison has been studied in [4], where a spectral density function A k ; !´has been calculated at di®erent temperatures. It occurs that at high temperature T ¹ t the functions A k ; !´obtained by QMC and in Hubbard-I paramagnetic solution are very similar.…”

“…With decreasing temperature, the di®erence between two A k ; !´functions becomes larger. For low temperature, the spin density wave (SDW) solution has been used in [4] for comparison to QMC data. It is known that SDW solution is valid in the weak correlation band limit U ½ W = zt and is not the appropriate solution in the SEC limit.…”