Coupled-Cluster Imaginary-Time Evolution and the Coupled-Cluster Energy Variance

TL;DR

This paper introduces a coupled-cluster imaginary-time evolution method that converges to standard solutions or provides additional insights, with the energy variance helping identify physically meaningful amplitudes.

Contribution

It develops a novel coupled-cluster imaginary-time evolution formalism and introduces the energy variance as a regularization tool for problematic solutions.

Findings

Evolution trajectories converge to standard coupled-cluster solutions when limits exist.

Energy variance minima identify physically regularized amplitudes.

Method demonstrated in single- and multi-reference coupled-cluster examples.

Abstract

We discuss a coupled-cluster formalism for carrying out imaginary-time evolution from an arbitrary reference, and study the properties of the resulting evolution trajectories. The evolution converges to a solution of the standard coupled-cluster amplitude equations in the long-time limit if a finite valued limit exists, but when such a limit does not exist, the trajectories still contain additional information beyond the standard solutions. We introduce the coupled-cluster energy variance which through its minima identifies physically regularized coupled-cluster amplitudes when the solutions of the amplitude equations are unreasonable. We demonstrate the value of this formalism in several exploratory examples within single- and multi-reference coupled-cluster formulations.