A driven similarity renormalization group approach to quantum many-body problems

TL;DR

This paper introduces a driven similarity renormalization group (DSRG) method for quantum many-body problems, offering computational advantages and demonstrating good accuracy for molecular properties, with some limitations in specific cases.

Contribution

The paper presents a novel integral DSRG approach, improving computational efficiency and extending SRG applications to electron correlation problems in quantum chemistry.

Findings

DSRG produces Hamiltonian flow similar to SRG.

Good agreement with benchmark CCSD(T) results for molecular properties.

Modified commutator approximation improves convergence issues.

Abstract

Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994), S. D. G{\l}azek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples [CCSD(T)]. Particularly surprising results are found when the SRG and DSRG methods are applied to C$_2$ and F$_2$. In the former case both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.