Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions

TL;DR

This paper compares high-order strong-coupling perturbation theory with dynamical mean-field theory for the Mott-Hubbard insulator, demonstrating excellent agreement and accuracy near the critical point in high dimensions.

Contribution

It provides the first large-scale combinatorial-diagrammatic computation of high-order contributions to the perturbation series for the Hubbard model, extending to the 15th order and extrapolating to infinite order.

Findings

Exact ground-state energy up to 15th order in 1/U

Excellent agreement between perturbation theory and DMFT methods

Accurate determination of critical behavior near the Mott transition

Abstract

We present a large-scale combinatorial-diagrammatic computation of high-order contributions to the strong-coupling Kato-Takahashi perturbation series for the Hubbard model in high dimensions. The ground-state energy of the Mott-insulating phase is determined exactly up to the 15-th order in 1/U. The perturbation expansion is extrapolated to infinite order and the critical behavior is determined using the Domb-Sykes method. We compare the perturbative results with two dynamical mean-field theory (DMFT) calculations using a quantum Monte Carlo method and a density-matrix renormalization group method as impurity solvers. The comparison demonstrates the excellent agreement and accuracy of both extrapolated strong-coupling perturbation theory and quantum Monte Carlo based DMFT, even close to the critical coupling where the Mott insulator becomes unstable.