A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917557625159680 |
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| author | Marécat, Quentin Saubanère, Matthieu |
| author_facet | Marécat, Quentin Saubanère, Matthieu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches Marécat, Quentin Saubanère, Matthieu Strongly Correlated Electrons 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. |
| title | A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.13446 |