A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches

TL;DR

This paper introduces a flexible unitary transformation framework to optimize bath orbital construction in density-matrix based quantum embedding methods, improving the physical relevance and efficiency of the embedding process.

Contribution

It generalizes the Block-Householder transformation with additional parameters, enabling optimized bath orbitals in quantum embedding approaches.

Findings

Enhanced bath orbital construction via parameter optimization.

Improved physical constraints fulfillment in bath orbitals.

Demonstrated effectiveness in the 1D Hubbard model.

Abstract

The performance of embedding methods is directly tied to the quality of the bath orbitals construction. In this paper, we develop a versatile framework, enabling the investigation of the optimal construction of the orbitals of the bath. As of today, in state-of-the-art embedding methods, the orbitals of the bath are constructed by performing a Singular Value Decomposition (SVD) on the impurity-environment part of the 1RDM, as originally presented in Density Matrix Embedding Theory (DMET). Recently, the equivalence between the SVD protocol and the use of unitary transformation, the so-called Block-Householder transformation, has been established. We present a generalization of the Block-Householder transformation by introducing additional flexible parameters. The additional parameters are optimized such that the bath-orbitals fulfill physically motivated constrains. The efficiency of the approach is discussed and exemplified in the context of the half-filled Hubbard model in one-dimension.