Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian

Abstract

The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

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• 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
• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
• A digital quantum simulation of the Agassi model
• Combining symmetry breaking and restoration with configuration interaction: extension to z-signature symmetry in the case of the Lipkin Model
• Phase diagram of an extended Agassi model
• Number conserving particle-hole RPA for superfluid nuclei