Self-consistent on-site and inter-site Hubbard parameters within DFT+U+V for UO$_2$ using density-functional perturbation theory
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To apply the Hubbard-corrected density-functional theory for predicting some known materials' properties, the Hubbard parameters are usually so tuned that the calculations give results in agreement with some experimental data and then one uses the tuned model to predict unknown properties. However, in designing new unknown novel materials there is no data to fit the parameters and therefore self-consistent determination of these parameters is crucial. In this work, using the new method formulated by others, which is based on density-functional perturbation theory, we have calculated self-consistently the Hubbard parameters for UO$_2$ crystal within different popular exchange-correlation approximations. The calculated ground-state lattice constants and electronic band-gaps are compared with experiment and shown that PBE-sol lead to results in best agreement with experiment.Keywords:
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The effect of electron correlations on the antiferromagnetic ground state of a half-filled Hubbard model is examined by means of two approximate ways; Gutzwiller's variational method and the perturbational method. Both results by the two ways indicate that the antiferromagnetism is not destroyed by correlation effect in the limit of weak interaction.
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t-J model
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The Gutzwiller conjugate gradient minimisation (GCGM) theory is an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. Previous applications of GCGM provides satisfying accuracy of ground-state energy of Hubbard models. In the current work, we address the problem of whether the obtained wave function is a good approximation for the true ground state by comparing the correlation functions with the benchmark data. Our results confirms the accuracy of the reproduced ground state of the regular Hubbard model, but with some exception for the frustrated Hubbard model.
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Abstract Using Bogolyubov's variational principle and the mean‐field theory the properties of the ground state in the Hubbard‐Hirsch model are discussed for weak coupling condition, and the phase diagrams are plotted. It is pointed out that the ground state of the system can be paramagnetic, ferromagnetic, or antiferromagnetic, depending on the intensity of the Coulomb interaction U and the exchange interaction J ; the charge‐ordered phase does not exist.
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We study the ground state of the two-dimensional (2D) disordered Hubbard model by means of the projector quantum Monte Carlo (PQMC) method. This approach allows us to investigate the ground state properties of this model for lattice sizes up to $10 \times 10$, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-1/2 fermions remains localised in the presence of the short-ranged Hubbard interaction.
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By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.
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We consider the one-orbital N -site repulsive Hubbard model on two kagome like chains, both of which yield a completely dispersionless (flat) one-electron band.Using exact many-electron ground states in the subspaces with n ≤ nmax (nmax ∝ N ) electrons, we calculate the square of the total spin in the ground state to discuss magnetic properties of the models.We have found that although for n < nmax the ground states contain fully polarized states, there is no finite region of electron densities n/N < 1 (N = N/3 or N = N/5) where ground-state ferromagnetism survives for N → ∞.
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For square (cubic) Hubbard lattice with infinite repulsion energy U exact result has been obtained: the ferromagnetic state with maximum total spin is not the ground state of system, if the hole number is equal to two.
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The exact result is obtained for a square (cubic) Hubbard lattice with an infinitely large repulsion energy U: the ferromagnetic state with the maximum spin is not the ground state of the system if the number of holes is equal to two.
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With a canonical transformation, the antiferromagnetic ground state and the electron-hole excitation energy gap of the conventional Hubbard model are transferred to describe the charge-ordered ground state and the similar excitation energy of a half-filled Hubbard model with negative $U$. The band-structure effect is also considered.
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