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

Abstract

Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994), S. D. Głazek 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.

References in corpus (10)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• In-Medium Similarity Renormalization Group for Nuclei
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
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• A canonical transformation theory from extended normal ordering
• Adaptive multiconfigurational wave functions
• Unitary Correlation Operator Method and Similarity Renormalization Group: Connections and Differences
• Block Diagonalization using SRG Flow Equations
• Time-dependent coupled-cluster method for atomic nuclei
• Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces

Cited by in corpus (5)

• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Excited states using semistochastic heat-bath configuration interaction
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Ab initio Gamow in-medium similarity renormalization group with resonance and continuum
• Addition and removal energies of circular quantum dots