Ab Initio Excited States from the In-Medium Similarity Renormalization Group

Abstract

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of $1$p$1$h excitations) becomes exact for a subset of eigenvalues. In the second approach, equations-of-motion (EOM) techniques are applied to the ground-state-decoupled IMSRG Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two-dimensions and the closed shell nuclei ${}^{16}$O and ${}^{22}$O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster (EOM-CC) calculations, which paves the way for more interesting applications of the EOM-IMSRG to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within 1-2 nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

16 pages, 13 figures

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Cited by in corpus (16)

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• Ab initio electromagnetic observables with the in-medium similarity renormalization group
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• Improved many-body expansions from eigenvector continuation
• Ab initio Gamow in-medium similarity renormalization group with resonance and continuum
• Computing the dipole polarizability of 48Ca with increased precision
• Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches
• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Factorized Approximation to the IMSRG(3)
• Nuclear Structure from the In-Medium Similarity Renormalization Group
• Coupled cluster theory for the ground and excited states of two dimensional quantum dots
• Addition and removal energies of circular quantum dots
• Ab initio calculations of monopole sum rules: From finite nuclei to infinite nuclear matter
• From closed shells to open shells: Coupled-cluster calculations of atomic nuclei
• Many-body calculations with Deuteron based single-particle bases and their associated natural orbits