Construction of Localized Basis for Dynamical Mean Field Theory

TL;DR

This paper introduces a new method for constructing a localized basis that optimizes the truncation of non-local interactions in dynamical mean field theory, improving first-principles material calculations.

Contribution

It proposes a criterion and algorithm for creating a localized basis to better apply dynamical mean field theory in first-principles calculations.

Findings

Tested on a toy model, the criterion was found satisfactory.

The localized basis enhances the accuracy of non-local interaction truncation.

The method facilitates more precise material property calculations from first principles.

Abstract

Many-body Hamiltonians obtained from first principles generally include all possible non-local interactions. But in dynamical mean field theory the non-local interactions are ignored, and only the effects of the local interactions are taken into account. The truncation of the non-local interactions is a basis dependent approximation. We propose a criterion to construct an appropriate localized basis in which the truncation can be carried out. This involves finding a basis in which a functional given by the sum of the squares of the local interactions with appropriate weight factors is maximized under unitary transformations of basis. We argue that such a localized basis is suitable for the application of dynamical mean field theory for calculating material properties from first principles. We propose an algorithm which can be used for constructing the localized basis. We test our criterion on a toy model and find it satisfactory.