Ground state of the frustrated Hubbard model within DMFT: energetics of Mott insulator and metal from ePT and QMC

TL;DR

This paper introduces a new extrapolation method, ePT, which, combined with QMC, provides highly precise energy and double occupancy estimates for the Hubbard model's Mott insulator and metallic states within DMFT.

Contribution

The paper develops ePT for extrapolating perturbative series and applies it with QMC to achieve unprecedented accuracy in ground state energetics within DMFT.

Findings

ePT reliably extrapolates strong-coupling PT to infinite order.

High-precision estimates of energy and double occupancy for Mott insulator.

Accurate ground state properties for metallic phase from QMC simulations.

Abstract

We present a new method, ePT, for extrapolating few known coefficients of a perturbative expansion. Controlled by comparisons with numerically exact quantum Monte Carlo (QMC) results, 10th order strong-coupling perturbation theory (PT) for the Hubbard model on the Bethe lattice is reliably extrapolated to infinite order. Within dynamical mean-field theory (DMFT), we obtain continuous estimates of energy E and double occupancy D with unprecedented precision O(10^{-5}) for the Mott insulator above its stability edge U_{c1}=4.78 as well as critical exponents. In addition, we derive corresponding precise estimates for E and D in the metallic ground state from extensive low-temperature QMC simulations using a fit to weak-coupling PT while enforcing thermodynamic consistency.