Density matrix embedding: A strong-coupling quantum embedding theory

TL;DR

This paper extends density matrix embedding theory (DMET) to full chemical Hamiltonians, enabling accurate quantum embedding of strongly coupled fragments and demonstrating its effectiveness on challenging hydrogen models.

Contribution

The authors develop a rigorous quantum bath approach within DMET for chemical systems, surpassing empirical methods and traditional embedding techniques.

Findings

Successfully applied DMET to hydrogen ring and grid models

Accurately described symmetric dissociation of hydrogen grid

Demonstrated effectiveness on strongly correlated systems

Abstract

We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett. 109 186404 (2012)] 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 4x3 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 of complex strongly coupled, strongly correlated systems in terms of their individual fragments.