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Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The resulting parametrization is shown to be in better agreement with highly precise data obtained from fully numerical solution of the Bethe-Ansatz equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402 (2003)]. Unlike these earlier proposals, the present parametrization correctly predicts a positive Mott gap at half filling for any U>0. The construction is extended to spin-dependent phenomena by parametrizing the magnetization-dependence of the ground-state energy using further exact results and numerical benchmarking. Lastly, the parametrizations developed for the spatially uniform model are extended by means of a simple local-density-type approximation to spatially inhomogeneous models, e.g., in the presence of impurities, external fields or trapping potentials. Results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost.
We investigate the effects of weak to moderate disorder on the T=0 Mott metal-insulator transition in two dimensions. Our model calculations demonstrate that the electronic states close to the Fermi energy become more spatially homogeneous in the cri
We study the dynamical response of the half-filled one-dimensional(1d) Hubbard model for a range of interaction strengths $U$ and temperatures $T$ by a combination of numerical and analytical techniques. Using time-dependent density matrix renormaliz
Using a straightforward extension of the analysis of Lieb and Wu, we derive a simple analytic form for the ground state energy of a one-dimensional Hubbard ring in the atomic limit. This result is valid for an textit{arbitrary} number of lattice site
We derived a simple metal-insulator criterion in analytical form for the doped Mott-Hubbard materials. Its readings closely related to the orbital and spin nature of the ground states of the unit cell. The available criterion readings (metal or insul
We study the second order finite temperature Mott transition point in the fully frustrated Hubbard model at half filling, within Dynamical Mean Field Theory. Using quantum Monte Carlo simulations we show the existence of a finite temperature second o