Adiabatic based Algorithm : a comprehensivealgorithmic description

Eric Bourreau, Gérard Fleury, Philippe Lacomme

Rachel Berkowitz

Atushi Tanaka

A bracket calculus for adiabatic descriptions of quantum composite systems is introduced. The bracket calculus recovers a consistent and transparent way to obtain various adiabatic representations, e.g. the adiabatic nuclear momentum representation, and the adiabatic Husimi function. Furthermore, it is shown that the bracket calculus touches on an issue of the choice of subsystems (“electrons” and “nuclei” in the adiabatic description of molecules.

K. T. Hecht

Mikuláš Matoušek

One of the more modern directions in quantum chemistry, which is mostly unexplored, is using Hamiltonians which include not only the electrons of the molecule, but also other quantum particles. These are also termed multicomponent Hamiltonians. The Density Matrix Renormalization Group method has become one of the mainline methods in multireference quantum chemistry. In this work we describe a way to extend the DMRG algorithm to use multicomponent Hamiltonians. We start by a description of the DMRG algorithm, showcasing the usage of quantum chemical DMRG on multiple challenging systems. We include a brief description how to extend the DMRG algorithm to also treat dynamical correlation with the Adiabatic Connection method. We then describe the extension of DMRG to multicomponent Hamiltonians which has been implemented by the author of this work, and finally show how DMRG can be useful for polaritonic chemistry, where the molecule interacts with the quantized states of light in an optical cavity.