Browsing by Author "Qiu, Yiheng"
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Item Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations(AIP Publishing LLC., 2016) Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.Spin-projected Hartree-Fock is written 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.Item Merging symmetry projection with coupled cluster theory(2018-08-31) Qiu, Yiheng; Scuseria, Gustavo EThe goal of electronic structure theory is to solve the time-independent Schrodinger equation with a method that scales polynomially with the system size. The problem has been solved in the weakly-correlated regime, where coupled cluster theory (CC) with singles, doubles and perturbative triples (CCSD(T)) can achieve chemical accuracy. However, in the strongly-correlated regime, where the two-body interaction dominates, there are still no methods that can achieve a comparable accomplishment. Strong correlation always comes hand in hand with spontaneous symmetry breaking in mean-field theory. For example, coupled cluster theory faces a symmetry dilemma in the strongly correlated regime, where it either completely fails to describe the system if symmetry adapted, or has to artificially break certain symmetries in order to produce reasonable energies. It is plausible that the problem of strong correlation can be solved by curing the symptoms, i.e., fixing the symmetries. Symmetry projection has been carried out at the mean-field level, but it was unclear until this work how to incorporate correlation on top of it because of the language barrier between symmetry projection and coupled cluster theory. This thesis is devoted to combining CC and symmetry projection, focusing on spin and number symmetry. Different flavours of theories are obtained depending on whether a restricted or unrestricted reference is used. On the restricted side, the spin projected unrestricted Hartree Fock (SUHF) state can be rewritten as a polynomial of particle-hole excitations, acting on the restricted reference. Thus, this formalism opens up many ways to combine SUHF with CC. One the unrestricted side, the concept of disentangled cluster is introduced to describe the CC wavefunction transformed by symmetry rotation. A scheme basing on differential equations is devised to approximate these disentangled clusters, which scales polynomially and is systematically improvable. By combining symmetry projection and coupled cluster theory, the symmetry dilemma can be solved to a good extent.Item Projected coupled cluster theory(AIP Publishing, 2017) Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo; Scuseria, Gustavo E.Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.Item Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection(AIP Publishing, 2018) Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo; Scuseria, Gustavo E.Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and coupled cluster theory for weak correlation offers tantalizing promise to account for both on an equal footing. In order to do so, however, the coupled cluster portion of the wave function must be optimized in the presence of the symmetry projection. This paper discusses how this may be accomplished, and shows the importance of doing so for both the Hubbard model Hamiltonian and the molecular Hamiltonian, all with a computational scaling comparable to that of traditional coupled cluster theory.Item Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory(AIP Publishing, 2017) Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.Projected Hartree-Fockﾠtheoryﾠprovides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems.ﾠCoupled clusterﾠtheory,ﾠin contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock andﾠcoupled clusterﾠtheoryﾠin a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.