Time-dependent coupled-cluster method for atomic nuclei

TL;DR

This paper develops a time-dependent coupled-cluster approach for nuclear physics, demonstrating conservation laws and applying it to model systems like He-4, O-16, and the Lipkin model to showcase its effectiveness.

Contribution

It explicitly demonstrates the conservation of observables in time-dependent coupled-cluster theory within nuclear physics and explores the role of the similarity-transformed Hamiltonian.

Findings

Observables commuting with the Hamiltonian are conserved during time evolution.

The method is successfully applied to small nuclear systems and models.

Imaginary time evolution relates to similarity renormalization group transformations.

Abstract

We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method.