Bath optimization in the Cellular Dynamical Mean Field Theory

TL;DR

This paper investigates optimal bath parameter selection in Cellular Dynamical Mean Field Theory (CDMFT) for strongly correlated systems, proposing a new merit function that improves modeling of the Mott transition.

Contribution

It introduces a new merit function weighted with the self-energy, enhancing the accuracy of CDMFT in capturing the Mott transition.

Findings

The new merit function better fits the Mott transition in two dimensions.

Using multiple merit functions can improve the self-consistency in CDMFT.

Preference for merit functions with minimal gradient of the self-energy functional.

Abstract

In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented by a small cluster of correlated sites, coupled to an adjustable bath of uncorrelated sites simulating the cluster's environment; the parameters governing the bath are set by a self-consistency condition involving the local Green function and the lattice electron dispersion. Solving the cluster problem with an exact diagonalization method is only practical for small bath sizes (8 sites). In that case the self-consistency condition cannot be exactly satisfied and is replaced by a minimization procedure. There is some freedom in the definition of the `merit function' to optimize. We use Potthoff's Self-Energy Functional Approach on the one- and two-dimensional Hubbard models to gain insight into the best choice for this merit function. We argue that several merit functions should be used and preference given to the one that leads to the smallest gradient of the Potthoff self-energy functional. We propose a new merit function weighted with the self-energy that seems to fit the Mott transition in two dimensions better than other merit functions.