Five years of density matrix embedding theory

Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. This chapter discusses the ground‐state and response theory formulations of DMET, and reviews several applications. In addition, it gives a proof that the local density of states can be obtained by working with a Fock space of bath orbitals. The chapter also reviews nomenclature and several concepts from quantum information theory, which are necessary to follow the discussion on DMET. The DMET algorithm is not limited to ground‐state properties, but can be extended to calculate response properties as well. The chapter extends the ground‐state algorithm to calculate Green's functions. Ground‐state DMET has been applied to a variety of condensed matter systems. It has been used to study the one‐dimensional Hubbard model, the one‐dimensional Hubbard‐Anderson model, the one‐dimensional Hubbard‐Holstein model, the two‐dimensional Hubbard model on the square as well as the honeycomb lattice, and the two‐dimensional spin-½ J₁‐J₂‐model