Nambu-Covariant Many-Body Theory II: Self-Consistent Approximations

Drissi, Mehdi; Rios, Arnau; Barbieri, C.

doi:10.48550/arxiv.2107.09763

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…More importantly, the combined use of Nambu indices and an appropriate dual basis can be extended into a generalised Nambu-covariant formalism as discussed in Refs. [40,41]. In Nambu-covariant Green's function theory, all normal and anomalous propagators appear as specific elements of a unique propagator carrying the common features in their spectral representations.…”

Section: Gorkov Green's Function Formalismmentioning

confidence: 99%

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Gorkov algebraic diagrammatic construction formalism at third order

Barbieri,

Duguet,

Somà

2021

Preprint

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Background: The Gorkov approach to self-consistent Green's function theory has been formulated in [V. Somà, T. Duguet, C. Barbieri, Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principle computations of semi-magic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number non-conserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences (i.e. two neutron separation energies, excitation energies of states dominating the one-nucleon spectral function), ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of N ±1 particle systems or delicate quantities such as secondorder energy differences associated to pairing gaps, requires to go to higher truncation orders.Purpose: The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians. Methods:The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy.Results: Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian. Conclusion:Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.

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Section: Gorkov Green's Function Formalismmentioning

confidence: 99%

“…This choice differs from our initial Gorkov work of Ref [25]. but maintains a continuity of notation with our other SCGF developments[16,23,[34][35][36][37][38][39][40][41]…”

mentioning

confidence: 99%

Gorkov algebraic diagrammatic construction formalism at third order

Barbieri,

Duguet,

Somà

2021

Preprint

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“…In spite of their great versatility, current implementations of SCGF face some limitations in the pairing instabilities for symmetric matter at very low temperatures and densities, and in the precision of response functions that would require effective vertices to go beyond resummations of dressed ring diagrams. While some step could be taken using a Nambu covariant formalism [29], these problems may be solved more efficiently using a direct digonalization in the full Fock space that goes beyond common post-Hartree-Fock (PHF) many-body truncations.…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces

Arthuis¹,

Barbieri²,

Pederiva³

et al. 2022

Preprint

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Neutron matter, through its connection to neutron stars as well as systems like cold atom gases, is one of the most interesting yet accessible systems in nuclear physics. The Configuration-Interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing to tackle strongly coupled systems. In contrast to other Quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of non-local interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations with low resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.

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Nambu-Covariant Many-Body Theory II: Self-Consistent Approximations

Cited by 2 publications

References 3 publications

Gorkov algebraic diagrammatic construction formalism at third order

Gorkov algebraic diagrammatic construction formalism at third order

Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces

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