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Hole Pockets in the Doped 2D Hubbard Model

Adriana Moreo, Daniel Duffy

Published Jan 1, 1994• 2 citations
OpenAlex

Abstract

The electronic momentum distribution n(k) of the two dimensional Hubbard model is studied for different values of the coupling U/t, electronic density 〈n〉, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on 8 × 8 clusters shows that features consistent with hole pockets at momenta k = ( ± π

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Europhysics Letters (EPL)•Mar 1, 1991•8 citations
The electronic momentum distribution n(k) of the two-dimensional (2D) Hubbard model is studied for different values of the coupling U/t, electronic density 〈n〉, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on 8\ifmmode\times\else\texttimes\fi{}8 clusters shows that along the line from (0,\ensuremath{\pi}) to (\ensuremath{\pi},0) a minimum in n(k) at momenta k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) appears as the system is doped away from half-filling. In the range of couplings studied, the depth of this minimum is the largest at density 〈n〉\ensuremath{\approxeq}0.9, and it increases with decreasing temperature. Its existence is correlated with the strength of the antiferromagnetic correlations in the system. The apparent absence of structure at k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) in previous numerical studies of this model is explained. The results discussed here, together with the recent experimental data for the cuprates discussed by Aebi et al. [Phys. Rev. Lett. 72, 2757 (1994)], reopens the possibility that hole pockets exist in the doped 2D Hubbard model, although more evidence is needed to fully demonstrate their existence.
Quantum Monte Carlo is used to calculate various pairing correlations of the 2D Hubbard model possessing band features experimentally observed in the cuprates. In the hole-doped case, where the Fermi level lies close to the van Hove singularities around (0,π)(0,π)(0,π), the dx2−y2_{x^2-y^2}x2−y2​ pairing correlation is selectively enhanced, while in the electron-doped case, where the singularities are far below the Fermi level and the Fermi surface runs through (±π/2,±π/2)(\pm π/2,\pm π/2)(±π/2,±π/2), both dx2−y2_{x^2-y^2}x2−y2​ and dxy_{xy}xy​ correlations are enhanced with the latter having a 2×2\sqrt{2}\times \sqrt{2}2​×2​ structure. The two pairing symmetries can mix to result in a nodeless gap.
The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.
We calculate with quantum Monte Carlo methods the Hall coefficient RH{R}_{H}RH​ for the 2D Hubbard model at small hole doping near half filling. In the weak coupling regime RH{R}_{H}RH​ is electronlike. In the strong coupling regime, where the mapping to the ttt- JJJ model is justified, RH{R}_{H}RH​ is electronlike with small amplitude in the temperature regime T>UT>UT>U, T<JT<JT<J and holelike in the temperature regime J<T<UJ<T<UJ<T<U. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers.
On the basis of quantum Monte Carlo simulations we study the influence of "breathing" lattice distortions on the two-dimensional Hubbard model. In the half-filled band case the system remains stable against the formation of a charge-density wave already for intermediate values (U=4tU=4tU=4t) of the electronic interaction. However, the addition of holes allows for a charge-density-wave state. Thus, the structural instability is not driven by nesting of the Fermi surface, but by the combined effect of doping and Coulomb correlation. The influence of the distortion on the various pairing correlation functions is calculated.
I present a scheme for performing weak-coupling expansions for the Hubbard model on square clusters near half-filling. Using this scheme the 6 × 6 cluster with 2, 3 and 4 holes is considered. I have calculated the ground-state quantum numbers for the 3- and 4-hole cases. In the 3-hole case I find a nonzero momentum near the (±π/2, ±π/2) points, while for the four-hole case the momentum is (0, 0). The calculation of low-lying excited states indicates the opening of a spin gap as one dopes away from half-filling.