Fictive Impurity Approach to Dynamical Mean Field Theory: a Strong-Coupling Investigation

TL;DR

This paper evaluates different cluster dynamical mean field theory methods for the Hubbard model at strong coupling, highlighting their strengths and limitations in capturing intersite spin correlations and spectral properties.

Contribution

It provides a comparative analysis of real space and momentum space approaches, identifying the pole structure issue and assessing their accuracy in a strong-coupling regime.

Findings

One real space method shows slow convergence and unphysical spectral states.

Momentum space representation better approximates intersite energy terms.

Neither method achieves high accuracy or uniform convergence.

Abstract

Quantum Monte Carlo and semiclassical methods are used to solve two and four site cluster dynamical mean field approximations to the square lattice Hubbard model at half filling and strong coupling. The energy, spin correlation function, phase boundary and electron spectral function are computed and compared to available exact results. The comparision permits a quantitative assessment of the ability of the different methods to capture the effects of intersite spin correlations. Two real space methods and one momentum space representation are investigated. One of the two real space methods is found to be significantly worse: in it, convergence to the correct results is found to be slow and, for the spectral function, nonuniform in frequency, with unphysical midgap states appearing. Analytical arguments are presented showing that the discrepancy arises because the method does not respect the pole structure of the self energy of the insulator. Of the other two methods, the momentum space representation is found to provide the better approximation to the intersite terms in the energy but neither approximation is particularly acccurate and the convergence of the momentum space method is not uniform. A few remarks on numerical methods are made.