Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions

Abstract

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization' scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at $U_{\mathrm{c}}=4.43\pm 0.05$. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent $\alpha =1/2$ in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott--Hubbard insulator.

arXiv comment22 pages, 16 figures; minor changes (one reference added, included comparison with Falicov-Kimball model)

References in corpus (11)

• Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
• Finite temperature numerical renormalization group study of the Mott-transition
• The Finite Temperature Mott Transition in the Hubbard Model in Infinite Dimensions
• Correlation Induced Insulator to Metal Transitions
• Transport Properties of the Infinite Dimensional Hubbard Model
• Absence of hysteresis at the Mott-Hubbard metal-insulator transition in infinite dimensions
• Mott-Hubbard transition in infinite dimensions
• Density of states near the Mott-Hubbard transition in the limit of large dimensions
• Critical behaviour near the metal-insulator transition of a doped Mott insulator
• Insulating phases of the infinite-dimensional Hubbard model
• Coexistence of solutions in dynamical mean-field theory of the Mott transition

Cited by in corpus (16)

• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions
• Electron spectra close to a metal-to-insulator transition
• Single-Particle Dynamics in the Vicinity of the Mott-Hubbard Metal-to-Insulator Transition
• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
• The Mott insulator - 10th order perturbation theory extended to infinite order using QMC
• Signatures of coherent electronic quasiparticles in the paramagnetic Mott insulator
• Zero temperature dynamics of the Hubbard model in infinite dimensions: A local moment approach
• Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory
• Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime
• Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit
• Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions
• Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory
• Charge dynamics in magnetically disordered Mott insulators
• Random dispersion approximation for the Hubbard model
• Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions