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Physical review. B, Condensed matter

Existence of hole pockets in the two-dimensional Hubbard model

Daniel Duffy, Adriana Moreo

Published May 1, 1995• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.51.11882

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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.
Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.
Quantum Monte Carlo results for the specific heat c of the two-dimensional Hubbard model are presented. At half filling it was observed that c\ensuremath{\sim}T2{\mathrm{T}}^{2}T2 at very low-temperatures. Two distinct features were also identified: a low-temperature peak related to the spin degrees of freedom and a higher-temperature broad peak related to the charge degrees of freedom. Away from half filling the spin-induced feature slowly disappears as a function of hole doping while the charge feature moves to lower temperature. A comparison with experimental results for the high-temperature cuprates is discussed.
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to T=t20T=\frac{t}{20}T=20t​ (t=hoppingt=\mathrm{hopping}t=hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion UUU. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.
We study the temperature and doping dependence of the two-dimensional (2D) Hubbard model in the intermediate coupling regime (U=4).(U=4).(U=4). As temperature is decreased for a half-filled band, 2D critical spin fluctuations give rise to a strong local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({k}_{F},\ensuremath{\omega})|$ at $\ensuremath{\omega}=0,$ leading to a split peak in the spectral function. These strong fluctuations dominating near half filling are completely destroyed by 12% doping concentration. Below this concentration the imaginary part of the self-energy vanishes nearly quadratically in frequency at the Fermi energy, a Fermi-liquid-like feature. With varying the temperature at this concentration, we present numerical evidence for the band Kondo effect in the doped 2D Hubbard model by showing at low temperatures a growing peak in the density of states, nearly quadratically vanishing (in frequency) scattering rates at the Fermi energy and a linearly vanishing (in temperature) effective magnetic moment.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.