Coupled Cluster Approximation to the \emph{t-J} Model

James J. Shepherd, Andreas Grüneis

We numerically examine divergences of the total energy in metallic systems of approximate many-body theories using Hartree--Fock as a reference, including perturbative (M\oller-Plesset, MP), coupled cluster (CC) and configuration interaction (CI) approaches. Controlling for finite size effects and basis set incompleteness error by comparison with energies from the random phase approximation (RPA), we suggest convincingly that non-perturbative coupled cluster theories are acceptable for modelling electronic interactions in metals whilst perturbative coupled cluster theories are not. Data are provided from the RPA with which it is possible to test other approximate finite-basis methods for divergences with only modest computational cost.

Janice D. Prie, Jay D. Mancini, Yuan Zhou +1 more

Bo Peng, Karol Kowalski

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

David J. Dean

Mihály Kállay, Péter R. Śurján

The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction (CI). CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments [J. Chem. Phys. 113, 1359 (2000)] the operation count of this new method scales roughly as the (2n+2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is also discussed.

Isaiah Shavitt, Rodney J. Bartlett