Three Lagrangians for the complete-active space coupled-cluster method

TL;DR

This paper introduces three variational formulations of the CASCC method, enabling better approximation of model vectors and potential to overcome exponential scaling barriers in multireference quantum chemistry calculations.

Contribution

It presents new variational formulations for CASCC that incorporate smooth manifold approximations, including matrix-product states, enhancing scalability and accuracy.

Findings

Allows systematic correction of coupled-cluster and DMRG methods.

Enables favorable-scaling multireference coupled-cluster calculations.

Extends formulations to time-dependent quantum dynamics.

Abstract

Three fully variational formulations of the complete-active space coupled-cluster (CASCC) method are derived. The formulations include the ability to approximate the model vectors by smooth manifolds, thereby opening up the possibility for overcoming the exponential wall of scaling for model spaces of CAS type. In particular, model vectors of matrix-product states are considered, and it is argued that the present variational formulation allows not only favorably-scaling multireference coupled-cluster calculations, but also systematic correction of tailored coupled-cluster calculation and of quantum chemical density-matrix renormalization group methods, which are fast and polynomial scaling, but lacks the ability to properly resolve dynamical correlation at chemical accuracy. The extension of the variational formulations to the time-domain is also discussed, with derivations of abstract evolution equations.