Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum

Abstract

We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference coupled cluster theory and projected Hartree-Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy {\it and} norm kernels for which naturally terminating coupled-cluster expansions could be eventually obtained. The present work focuses on $SU(2)$ but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to $U(1)$ symmetry associated with particle number conservation. This is relevant to Bogoliubov coupled cluster theory that was recently formulated and applied to singly open-shell nuclei.

arXiv comment45 pages, 31 figures; to be published in Journal of Physics G: Nuclear and Particle Physics

References in corpus (47)

• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Self-consistent Green's function method for nuclei and nuclear matter
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Quantum Monte Carlo calculations of A=8 nuclei
• Recent developments in no-core shell-model calculations
• In-Medium Similarity Renormalization Group for Nuclei
• Projected Hartree-Fock Theory
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Nonperturbative shell-model interactions from the in-medium similarity renormalization group
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• Global study of quadrupole correlation effects
• Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions
• Coupled-cluster theory for three-body Hamiltonians
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Ab Initio Path to Heavy Nuclei
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• Leading chiral three-nucleon forces along isotope chains in the calcium region
• Ab-initio coupled-cluster effective interactions for the shell model: Application to neutron-rich oxygen and carbon isotopes
• Isotopic chains around oxygen from evolved chiral two- and three-nucleon interactions
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Particle-Number Projection and the Density Functional Theory
• Coupled cluster calculations of ground and excited states of nuclei
• Particle-Number Restoration within the Energy Density Functional Formalism
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
• Self-consistent Green's functions formalism with three-body interactions
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Benchmark Calculations for the Triton Binding Energy for Modern NN Forces and the pi-pi Exchange Three-Nucleon Force
• Triton calculations with the new Nijmegen potentials
• Quasiparticle Coupled Cluster Theory for Pairing Interactions
• Ab initio coupled-cluster study of 16-O
• Complex coupled-cluster approach to an ab-initio description of open quantum systems
• Ab Initio Calculations of Medium-Mass Nuclei with Explicit Chiral 3N Interactions
• Shell-model calculations for the three-nucleon system
• ROHF Theory Made Simple
• Coupled-cluster calculations for valence systems around O-16
• Ab initio coupled-cluster theory for open-shell nuclei
• Faddeev description of two-hole one-particle motion and the single-particle spectral function
• Microscopic self-energy calculations and dispersive optical-model potentials
• Faddeev treatment of long-range correlations and the one-hole spectral function of O16
• Time-dependent coupled-cluster method for atomic nuclei
• Breaking and restoring symmetries within the nuclear energy density functional method
• The nuclear energy density functional formalism
• Generator Coordinate Truncations
• Ab initio no-core shell model and microscopic reactions: recent achievements
• Goldstone-Brueckner Perturbation Theory Extended in Terms of Mixed Non-Orthogonal Slater-Determinants
• Three-nucleon forces in exotic open-shell isotopes
• Self-consistent Green's function calculation of 16O at small missing energies

Cited by in corpus (61)

• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• Radii and binding energies in oxygen isotopes: a puzzle for nuclear forces
• Symmetry restoration in mean-field approaches
• Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians
• Charge radii of exotic neon and magnesium isotopes
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
• Coupled-cluster calculations of neutrinoless double-beta decay in ${}^{48}$Ca
• Self-consistent Green's function theory for atomic nuclei
• Projected Coupled Cluster Theory
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian
• ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory
• Geminal-Based Configuration Interaction
• Correlating the Antisymmetrized Geminal Power Wave Function
• Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
• Ab Initio Derivation of Model Energy Density Functionals
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Moving away from singly-magic nuclei with Gorkov Green's function theory
• Bogoliubov many-body perturbation theory under constraint
• Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
• Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
• In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
• Normal-ordered $k$-body approximation in particle-number-breaking theories
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• On the norm overlap between many-body states. I. Uncorrelated overlap between arbitrary Bogoliubov product states
• Deformed in-medium similarity renormalization group
• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Tensor-decomposition techniques for ab initio nuclear structure calculations. From chiral nuclear potentials to ground-state energies
• Projected Coupled Cluster Theory: Optimization of cluster amplitudes in the presence of symmetry projection
• Construction of linearly independent non-orthogonal AGP states
• AGP-based unitary coupled cluster theory for quantum computers
• Effective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei
• Nuclear Structure from the In-Medium Similarity Renormalization Group
• Gorkov algebraic diagrammatic construction formalism at third order
• Second-order perturbation theory with spin-symmetry projected Hartree-Fock
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Ab initio-driven nuclear energy density functional method. A proposal for safe/correlated/improvable parametrizations of the off-diagonal EDF kernels
• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
• ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory
• Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian
• Ab initio computations from ${}^{78}$Ni towards ${}^{70}$Ca along neutron number $N=50$
• Symmetry-projected cluster mean-field theory applied to spin systems
• Calibration of Energy Density Functionals with Deformed Nuclei
• Variational theory combining number-projected BCS and coupled-cluster doubles
• Combining symmetry breaking and restoration with configuration interaction: extension to z-signature symmetry in the case of the Lipkin Model
• Impact of correlations on nuclear binding energies
• Structure and dynamics of open-shell nuclei from spherical coupled-cluster theory
• A Power Series Approximation in Symmetry Projected Coupled Cluster Theory
• Symmetry restoration methods
• Symmetry-restored Skyrme-Random-Phase-Approximation calculations of the monopole strength in deformed nuclei
• Nambu-Covariant Many-Body Theory II: Self-Consistent Approximations
• Symmetry projection to coupled-cluster singles and doubles wave function through the Monte Carlo method
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions
• From closed shells to open shells: Coupled-cluster calculations of atomic nuclei
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems
• Symmetry breaking and restoration on a fermionic quantum ring