Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations

Abstract

Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.

References in corpus (2)

• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

Cited by in corpus (7)

• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• Correlating the Antisymmetrized Geminal Power Wave Function
• Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
• Cluster decomposition of full configuration interaction wave functions: a tool for chemical interpretation of systems with strong correlation
• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
• Minimal matrix product states and generalizations of mean-field and geminal wavefunctions
• Addressing Strong Correlation by Approximate Coupled-Pair Methods with Active-Space and Full Treatments of Three-Body Clusters