Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory
arXiv:1009.4100 · doi:10.1103/PhysRevB.83.035120
Abstract
We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well with those from numerical Dynamical Density-Matrix Renormalization Group (DDMRG) calculations. The density of states of the lower Hubbard band also agrees very well with DDMRG data, apart from a resonance contribution at the upper band edge which cannot be reproduced in low-order perturbation theory.
40 pages, 7 figures
References in corpus (9)
- The numerical renormalization group method for quantum impurity systems
- A continuous-time solver for quantum impurity models
- Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
- Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory
- Electron spectra close to a metal-to-insulator transition
- Efficiency of quantum Monte Carlo impurity solvers for dynamical mean-field theory
- The Mott insulator - 10th order perturbation theory extended to infinite order using QMC
- Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions
- Random dispersion approximation for the Hubbard model