Journal Article

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

Marécat, Quentin, Saubanère, Matthieu

2023

Overview

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.

• Publisher: MDPI AG,MDPI
• Subject: Chemical Sciences / Construction / Decomposition / Density / density matrix embedding theory / divide-and-conquer algorithm / effective Hamiltonian / Eigenvalues / Embedding / Householder transformations / Hubbard model / one-body reduced density matrix functional embedding / Orbitals / Parameters / Physics / Singular value decomposition / unitary transformation