A Versatile Unitary Transformation Framework for an Optimal Bath Construction in Density-Matrix Based Quantum Embedding Approaches

The performance of embedding methods is directly tied to the quality of the bath orbital 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 one-body reduced density matrix, as originally presented in Density Matrix Embedding Theory. 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 constraints. The efficiency of the approach is discussed and exemplified in the context of the half-filled Hubbard model in one-dimension.