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Register a new userApproximate expression for the ground-state energy of the two- and three-dimensional Hubbard model at arbitrary filling obtained from dimensional scaling
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We generalize the linear discrete dimensional scaling approach for the repulsive Hubbard model to obtain a nonlinear scaling relation that yields accurate approximations to the ground-state energy in both two and three dimensions, as judged by comparison to auxiliary-field quantum Monte Carlo (QMC) data. Predictions are made for the per-site ground-state energies in two and three dimensions for $n$ (filling factor) and $U$ (Coulomb interaction) values for which QMC data are currently unavailable.
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We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly adopted Gutzwiller approximation (GA), which is a major source of inaccuracy. Instead, the theory uses an approximation that is based on the occupation probability of the on-site configurations, rather than approximations that decouple the site-site correlations as used in the GA. We test the theory in the one-dimensional and two-dimensional Hubbard models at various electron densities and find that GCGM reproduces energies and double occupancies in reasonable agreement with benchmark data at a very small computational cost.
We propose a new combined approach of the exact diagonalization, the renormalization group and the Bethe ansatz for precise estimates of the charge gap $Delta$ in the one-dimensional extended Hubbard model with the onsite and the nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $Delta$ including the prefactor without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $Delta$ is exponentially small, beyond usual renormalization group methods and/or finite size scaling approaches. The detailed results of $Delta$ down to of order of $10^{-10}$ near the MIT are shown as contour lines on the $U$-$V$ plane.
We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ at quarter filling using the density-matrix renormalization group method combined with a variational principle. Our numerical results for the Hubbard model (V=0) agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap $Delta_c$ and the correlation length $xi$ which controls this exponential decay.
The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the $(U,g_{rm ph})$ plane for the phonon-mediated interaction $g_{rm ph}$ and the Coulomb interaction $U$. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency $omega_0$. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical $ U^*approx g^*_{rm ph}$, followed at larger $Usim g_{rm ph}$ by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on $U$. For the Peierls-Hubbard model, the region of the $(U,g_{rm ph})$ plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency $omega_D$ decreases. A power law dependence $g_{rm ph} sim U^{2eta}$ is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term $V$ is added to the Hubbard interaction.
In order to understand the properties of Mott insulators with strong ground state orbital fluctuations, we study the zero temperature properties of the SU(4) spin-orbital model on a square lattice. Exact diagonalizations of finite clusters suggest that the ground state is disordered with a singlet-multiplet gap and possibly low-lying SU(4) singlets in the gap. An interpretation in terms of plaquette SU(4) singlets is proposed. The implications for LiNiO_2 are discussed.
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