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We present a review of the Quantum Monte Carlo results on the magnetic, charge and single-particle excitations as well as the pairing correlations of the two-dimensional Hubbard model. We are particularly interested in how these quantities are related to each other in the metallic state that forms near half-filling. These results are helpful in gaining a better understanding of the low energy excitations of the superconducting cuprates.
Physical Review B
Quantum Monte Carlo study of a nonmagnetic impurity in the two-dimensional Hubbard model2015 •
2006 •
The two-dimensional Hubbard model is studied within the Composite Operator Method (COM) with the residual self-energy computed in the Self-Consistent Born Approximation (SCBA). COM describes interacting electrons in terms of the new elementary excitations appearing in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. The anomalous features appearing in the spectral function A(k,\omega), the momentum distribution function n(k) and the Fermi surface are analyzed for various values of the filling (from overdoped to underdoped region) in the intermediate coupling regime at low temperatures. For low doping, in contrast with the ordinary Fermi-liquid behavior of a weakly-correlated metal found at high doping, we report the opening of a pseudogap and some non-Fermi-liquid features as measured for cuprates superconductors. In addition, we show the presence of kinks in the calculated electronic dispersion in agreement with ARPES data.
Physical Review Letters
Pseudogap and Spin Fluctuations in the Normal State of the Electron-Doped Cuprates2004 •
Physical Review B
Comparing pertinent effects of antiferromagnetic fluctuations in the two- and three-dimensional Hubbard model2009 •
We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the noninteracting limit is significantly broadened by the electronic correlations but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green’s function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.
Physical Review B
Excitations and response functions of the doped two-dimensional Hubbard model: A random-phase-approximation anaylsis1992 •
Physical Review B
Antiferromagnetically driven electronic correlations in iron pnictides and cuprates2009 •
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