Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian

Abstract

While coupled cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ameliorated by permitting the mean-field reference to break physical symmetries. Symmetry-broken coupled cluster, e.g. Bogoliubov coupled cluster, theory can indeed provide reasonably accurate energetic predictions, but the broken symmetry can compromise the quality of the resulting wave function and predictions of observables other than the energy. Merging symmetry projection and coupled cluster theory is therefore an appealing way to describe strongly correlated systems. Independently, two different but related formalisms have been recently proposed to achieve this goal. The two formalisms are contrasted in this manuscript, with results tested on the Richardson pairing Hamiltonian. Both formalisms are based on the disentangled cluster representation of the symmetry-rotated coupled cluster wavefunction. However, they differ in the way that the disentangled clusters are solved. One approach sets up angle-dependent coupled cluster equations, while the other involves first-order ordinary differential equations. The latter approach yields energies and occupation probabilities significantly better than those of number-projected BCS and BCS coupled cluster and, when the disentangled clusters are truncated at low excitation levels, has a computational cost not too much larger than that of BCS coupled cluster. The high quality of results presented in this manuscript indicates that symmetry-projected coupled cluster is a promising method that can accurately describe both weakly and strongly correlated finite many-fermion systems.

arXiv comment20 pages, 9 figures (1 figure added)

References in corpus (11)

• 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
• Quasiparticle Coupled Cluster Theory for Pairing Interactions
• Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
• Projected Coupled Cluster Theory
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
• Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry
• Projected Hartree-Fock as a Polynomial of Particle-Hole Excitations and Its Combination With Variational Coupled Cluster Theory
• Projected Coupled Cluster Theory: Optimization of cluster amplitudes in the presence of symmetry projection
• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian

Cited by in corpus (44)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• Symmetry restoration in mean-field approaches
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Symmetry assisted preparation of entangled many-body states on a quantum computer
• Correlating AGP on a quantum computer
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Geminal-Based Configuration Interaction
• Efficient evaluation of AGP reduced density matrices
• Correlating the Antisymmetrized Geminal Power Wave Function
• Geminal replacement models based on AGP
• Moving away from singly-magic nuclei with Gorkov Green's function theory
• Bogoliubov many-body perturbation theory under constraint
• Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective
• Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory
• A coupled cluster framework for electrons and phonons
• Normal-ordered $k$-body approximation in particle-number-breaking theories
• Ab initio computations of strongly deformed nuclei around ${}^{80}$Zr
• Construction of linearly independent non-orthogonal AGP states
• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Zero-pairing limit of Hartree-Fock-Bogoliubov reference states
• AGP-based unitary coupled cluster theory for quantum computers
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Gorkov algebraic diagrammatic construction formalism at third order
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Ab initio computations from ${}^{78}$Ni towards ${}^{70}$Ca along neutron number $N=50$
• Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces
• State preparation of AGP on a quantum computer without number projection
• Importance truncation in non-perturbative many-body techniques
• Variational theory combining number-projected BCS and coupled-cluster doubles
• Coupled-cluster theory for strong entanglement in nuclei
• A Power Series Approximation in Symmetry Projected Coupled Cluster Theory
• Symmetry-restored Skyrme-Random-Phase-Approximation calculations of the monopole strength in deformed nuclei
• Unified description of pairing and quarteting correlations within the particle-hole-boson approach
• Nambu-Covariant Many-Body Theory II: Self-Consistent Approximations
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Symmetry projection to coupled-cluster singles and doubles wave function through the Monte Carlo method
• The normal state of attractive Fermi gases from coupled-cluster theory
• Ab initio Bogoliubov many-body perturbation theory: closed-form constraint on the average particle number
• From closed shells to open shells: Coupled-cluster calculations of atomic nuclei
• Symmetry conserving Coupled Cluster Doubles wave function and the Self-Consistent odd particle number RPA
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems