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

TL;DR

This paper introduces Wick&d, a computational tool for automating the derivation of fermionic many-body theories using general Fermi vacua, enabling efficient evaluation of complex quantum operators.

Contribution

Wick&d automates the derivation and implementation of fermionic many-body theories with a flexible approach to correlated references, improving efficiency and generality.

Findings

Successfully derived and implemented coupled cluster equations up to octuple excitations.

Automated the derivation of second-order DSRG-MRPT2.

Demonstrated applicability to both projective and Fock-space formalisms.

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).