# Symplectic integration and physical interpretation of time-dependent coupled-cluster theory

## TL;DR

This paper develops a Hamiltonian framework for time-dependent coupled-cluster theory, introduces a physical interpretation of its states, and evaluates numerical integrators, highlighting stability issues under strong external fields.

## Contribution

It formulates a classical Hamiltonian structure for time-dependent coupled-cluster theory and provides a physical interpretation of its states, addressing longstanding interpretational challenges.

## Key findings

- Symplectic integrator is stable under high-intensity laser pulses.
- Numerical instabilities arise from rapid amplitude increases during strong field interactions.
- System-dependent limits exist for external field strengths in simulations.

## Abstract

The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critial evaluation of the standard fourth-order Runge--Kutta scheme and the symplectic Gauss integrator of variable order is given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.