Density matrix embedding theory

{{Technical|date=December 2017}}

The density matrix embedding theory (DMET) is a numerical technique to solve strongly correlated electronic structure problems. By mapping the system to a fragment plus its entangled quantum bath, the local electron correlation effects on the fragment can be accurately modeled by a post-Hartree–Fock solver. This method has shown high-quality results in 1D- and 2D- Hubbard models,[http://chemists.princeton.edu/chan/software/dmet/ Density Matrix Embedding Theory (DMET)], [https://web.archive.org/web/20160304221717/http://chemists.princeton.edu/chan/software/dmet/ archived] from Princeton.edu, retrieved on 2015-09-07.

and in chemical model systems incorporating the fully interacting electronic Hamiltonian, including long-range interactions.

{{cite journal|last1=Knizia|first1=Gerald|last2=Chan|first2=Garnet K.-L.|title=Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory|journal=Journal of Chemical Theory and Computation|date=2012|volume=9|issue=3|pages=1428–1432|doi=10.1021/ct301044e|pmid=26587604|s2cid=22099769 |url=https://resolver.caltech.edu/CaltechAUTHORS:20170125-131915766|arxiv=1212.2679}}

The basis of DMET is the Schmidt decomposition for quantum states, which shows that a given quantum many-body state, with macroscopically many degrees of freedom, K, can be represented exactly by an Impurity model consisting of 2N degrees of freedom for N<Density matrix of the impurity model and effective lattice model projected onto the impurity cluster match. When this matching is determined self-consistently, U thus derived in principle exactly models the correlations of the system (since the mapping from the full Hamiltonian to the impurity Hamiltonian is exact).