Temperature and bath size in exact diagonalization dynamical mean field theory

TL;DR

This paper investigates how temperature and bath size affect the accuracy of exact diagonalization DMFT in modeling strongly correlated materials, establishing guidelines for their optimal choice across various systems.

Contribution

It systematically analyzes the influence of temperature and bath size in ED DMFT, providing criteria for their selection to ensure accurate results in multi-orbital and multi-site systems.

Findings

Two bath levels per orbital or site are sufficient at low temperatures (5-10 meV).

Larger orbital or site counts require fewer bath levels for accurate modeling.

The study offers practical guidelines for applying ED DMFT to complex materials.

Abstract

DMFT combined with finite-T exact diagonalization is one of the methods to describe electronic properties of strongly correlated materials. Because of the rapid growth of the Hilbert space, the size of the finite bath used to represent the infinite lattice is severely limited. In view of the increasing interest in the effect of multi-orbital and multi-site Coulomb correlations in transition metal oxides, high-Tc cuprates, iron-based pnictides, organic crystals, etc., it is appropriate to explore the range of temperatures and bath sizes in which ED provides accurate results for various system properties. The bath must be large enough to achieve a sufficiently dense level spacing, so that useful spectral information can be derived, especially close to the Fermi-level. For an adequate projection of the lattice Green's function onto a finite bath, the choice of the temperature is crucial. The role of these two key ingredients in ED DMFT is discussed for a wide variety of systems in order to establish the domain of applicability of this approach. Three criteria are used to illustrate the accuracy of the results: (i) the convergence of the self-energy with bath size, (ii) quality of the discretization of the bath Green's function, and (iii) comparisons with complementary results obtained via CTQMC DMFT. The materials comprise a variety of three- and five-orbital systems, as well as single-band Hubbard models for two-dimensional triangular, square and honeycomb lattices, where non-local Coulomb correlations are important. The main conclusion from these examples is that a larger number of correlated orbitals or sites requires a smaller number of bath levels. Down to temperatures of 5 to 10 meV (for typical band widths W=2 eV) two bath levels per correlated impurity orbital or site are usually adequate.