Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation

Abstract

While the well-established $GW$ approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly-correlated systems, the $T$-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe-Salpeter equations when one considers $T$-matrix quasiparticle energies as well as a $T$-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. Comparison with more conventional schemes as well as other wave function methods are also reported. Our results suggest that the $T$-matrix-based formalism performs best in few-electron systems where the electron density remains low.

arXiv comment10 pages, 6 figures

References in corpus (41)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• Reference Energies for Double Excitations
• Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach
• First-principles GW calculations for DNA and RNA nucleobases
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• Quasi-Particle Self-Consistent $GW$ for Molecules
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Ab-initio calculation of the electronic and optical excitations in polythiophene: effects of intra- and interchain screening
• Reference Energies for Intramolecular Charge-Transfer Excitations
• Electronic structure and magnetic properties of correlated metals: A local self-consistent perturbation scheme
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• LDA++ approach to electronic structure of magnets: correlation effects in iron
• Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation
• An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach
• Beyond the GW approximation: combining correlation channels
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Correlation energy for the homogeneous electron gas: exact Bethe-Salpeter solution and new approximate evaluation
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Full-Frequency GW without Frequency
• Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double
• Ab Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies
• Green functions and self-consistency: insights from the spherium model
• Range Separated Brueckner Coupled Cluster Doubles Theory
• Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel
• Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations
• Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies
• Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism
• Dynamical Kernels for Optical Excitations
• A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW +BSE and self-consistent RPA

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