Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory

2012/12/12 by Gerald Knizia, Garnet Kin-Lic Chan, Garnet Kin‐Lic Chan · 352 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical physics #Chemistry #Computer science #Density matrix #Dissociation (chemistry) #Eigenvalues and eigenvectors #Embedding #Hamiltonian (control theory) #Hamiltonian matrix #Mathematics #Physics #Quantum #Quantum entanglement #Quantum mechanics #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Symmetric matrix #cond-mat.str-el #physics.chem-ph #quant-ph

paper · pdf · doi:10.1021/ct301044e

published in Journal of Chemical Theory and Computation 9(3), 1428-1432 (American Chemical Society) · 5 pages, 4 figures

arxiv created 2012/12/12 · openalex publication_date 2013/02/21 · arxiv updated 2013/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating complex strongly coupled, strongly correlated systems in terms of their individual fragments.

Citations

• Frozen density functional approach for ab initio calculations of solvated molecules

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