Automatic derivation of fermionic many-body theories based on general Fermi vacua

Abstract

This paper describes Wick&d, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&d employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&d can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of Wick&d, we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory (DSRG-MRPT2).

References in corpus (5)

• Array Programming with NumPy
• A canonical transformation theory from extended normal ordering
• Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory
• Cavity-modulated ionization potentials and electron affinities from quantum electrodynamics coupled-cluster theory
• p${}^{†}$q: A tool for prototyping many-body methods for quantum chemistry

Cited by in corpus (12)

• Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
• Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations
• State-Specific Coupled-Cluster Methods for Excited States
• Towards accurate spin-orbit splittings from relativistic multireference electronic structure theory
• Equation Generator for Equation-of-Motion Coupled Cluster Assisted by Computer Algebra System
• Renormalized Internally-Contracted Multireference Coupled Cluster with Perturbative Triples
• Complete Active Space Iterative Coupled Cluster Theory
• Generating coupled cluster code for modern distributed memory tensor software
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Non-iterative Triples for Transcorrelated Coupled Cluster Theory
• Efficient Implementation of the Spin-Free Renormalized Internally-Contracted Multireference Coupled Cluster Theory
• SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities