Exploration of Time-dependent Coupled Cluster theory for the extraction of eigenvalues and eigenstate properties

Abstract

Eigenstate properties of time-independent Hamiltonians using Coupled Cluster (CC) theory are typically retrieved using Equations of Motion (EOM-CC) or equivalent response formalisms. Obtaining spectral information (such as energy eigenvalues) from time autocorrelation functions has long been explored in the vibrational spectral literature. The extraction of additional eigenstate properties (e.g., reduced density matrices) via time propagation has received less attention. We explore extracting eigenstate properties via Fourier analysis of time-propagated cluster amplitudes in model 1-body Hamiltonian systems. Demonstrating a particle statistic invariant approach to produce eigenstate reduced density matrices from the extracted t-amplitudes. We expand on the use of the thermofield-coupled cluster (TFCC), employing real-time propagation of TFCC states to parameterize t-amplitudes with explicit mappings onto reduced density matrices. We find that extracting eigenstate t-amplitudes for model fermionic, distinguishable, and bosonic systems is successful, with accuracy increasing as propagation length increased.

Continuing this exploration of quantum dynamics to recover eigenstate features, we further explore the use of a wall-clock time-efficient mixed (CC/configuration interaction (CI)) ansatz, previously used for vibronic systems, to probe single-surface vibrational Hamiltonians. We extend the ansatz and computational methods for quartic Hamiltonians to include quadruply excited CI operators. We determine that the ansatz cannot currently describe highly anharmonic systems via the investigation of a 1D double well potential. We further investigate the use of the ansatz's time efficiency to extract an accurate dense eigenspectrum from long-time propagated autocorrelation functions for 2 molecular systems. We demonstrate that a dense eigenspectrum can be recovered via single-mode specific initial displacements. Comparing autocorrelation spectra produced with the Mixed CC/CI ansatz against those from the state of the art Multiconfigurational Time-dependent Hartree (MCTDH), we find that the ansatz can reproduce near MCTDH-quality spectra for the CH$_3$CN system but demonstrates small pathologies CH$_2$NH.