Magnetic properties and temperature variation of spectra in the Hubbard model

Abstract

In the two-dimensional fermionic Hubbard model, temperature and concentration dependencies of the uniform magnetic susceptibility and squared site spin, the variation of the double occupancy with the repulsion and the temperature dependence of the spin structure factor are calculated using the strong coupling diagram technique. In these calculations, a correction parameter is introduced into the irreducible vertex to fulfill the Mermin-Wagner theorem and to attain low temperatures. Satisfactory agreement of the obtained results with data of Monte Carlo simulations, numerical linked-cluster expansions and experiments in optical lattices lends support to the validity of such a correction. The ability to attain low temperatures allows us to investigate spectral functions in this region. At half-filling, for small and large Hubbard repulsions no qualitative changes are observed in comparison with somewhat higher temperatures reached in the previous work. However, on cooling, there appears a new feature for moderate repulsions -a narrow band emerges near the Fermi level, which produces a pronounced peak in the density of states. By its location and bandwidth, the feature is identified with the spin-polaron band. PACS. xx.xx.xx xx

Negative electron compressibility in the Hubbard model

“…Due to the particle-hole symmetry of the considered model values of µ ≤ U/2 only will be considered below. DOSs calculated for µ T are similar to those obtained earlier with a somewhat different calculation procedure [12][13][14]. For half-filling, the Mott gap is seen around the Fermi level located at ω = 0 (Figures 1.2(a) and (b)).…”

Spin and charge fluctuations in the Hubbard model

“…After the FL enters the band, the peak is kept at the FL in a wide range of hole concentrations. Having regard to processes leading to the appearance of this peak and earlier results obtained in the one-band Hubbard [20,21] and the t-J models (see, e.g., [37][38][39]), it can be connected with spinpolaron states. They are bound states of holes and spin excitations.…”

The t−t′−t″−U Hubbard model and Fermi-level peak

“…The FL peak is not inherent solely to the t-t ′ -t ′′ -U model. In the previous work [34] it was revealed in the t-U Hubbard model. Ranges of chemical potentials and electron concentrations, in which AF fluctuations are strong and the peak is visible, are wider in the former model.…”

“…For somewhat higher T , as in the t-U model [14], the DOS at half-filling is inherent in a bad metal with a dip at the FL. Owing to a finite DOS at ω = 0, as the temperature decreases, the FL peak arises even at half-filling in this case both in the t-U [34] and t-t ′ -t ′′ -U models. As follows from Fig.…”

“…In [34], the parameter ζ was introduced in the second-order cumulant to remedy this defect. This amendment is determined by cumulants of higher orders, which form corrections to the used irreducible four-leg vertexthe second-order cumulant.…”