Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

Abstract

This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing a representative example on the driven similarity renormalization group (DSRG). Starting from the least approximate method - the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)] - we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-$n$ and -$n^{\prime }$ ($n=1,2,3,4$) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive quadratic commutators [qDSRG(2)]. The resulting qDSRG(2)+(T) approach matches the accuracy of the "gold-standard" coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.

References in corpus (11)

• A variational eigenvalue solver on a quantum processor
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Scalable Quantum Simulation of Molecular Energies
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• A canonical transformation theory from extended normal ordering
• A driven similarity renormalization group approach to quantum many-body problems
• Driven similarity renormalization group: Third-order multireference perturbation theory
• Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators

Cited by in corpus (9)

• In-medium similarity renormalization group with three-body operators
• Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies
• Factorized Approximation to the IMSRG(3)
• IMSRG with flowing 3 body operators, and approximations thereof
• A new "gold standard": perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing
• Renormalized Internally-Contracted Multireference Coupled Cluster with Perturbative Triples
• Complete Active Space Iterative Coupled Cluster Theory
• Assessing the Orbital-Optimized Unitary Ansatz for Density Cumulant Theory
• Equation-of-motion internally contracted multireference unitary coupled-cluster theory