Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Signoracci, Angelo J.; Duguet, Thomas; Hagen, Gaute; Jansen, G. R.

doi:10.1103/PhysRevC.91.064320

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Journal Article · Mon Jun 29 00:00:00 EDT 2015 · Physical Review C

DOI:https://doi.org/10.1103/PhysRevC.91.064320· OSTI ID:1265773

Signoracci, Angelo J. ^[1]; Duguet, Thomas ^[2]; Hagen, Gaute ^[1]; Jansen, G. R. ^[3]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Michigan State Univ., East Lansing, MI (United States)
Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an N_max=6 spherical harmonic oscillator basis for ^16,18O and ¹⁸Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while ²⁰O and ²⁰Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725; FG02-96ER40963; SC0008499

OSTI ID:: 1265773

Alternate ID(s):: OSTI ID: 1198603

Journal Information:: Physical Review C, Journal Name: Physical Review C Journal Issue: 6 Vol. 91; ISSN 2469-9985

Publisher:: APSCopyright Statement

Country of Publication:: United States

Language:: English

References (60)

Two-component Fermi systems: II. Superfluid coupled cluster theory Lahoz, W. A.; Bishop, R. F. Zeitschrift f�r Physik B Condensed Matter, Vol. 73, Issue 3 https://doi.org/10.1007/BF01314275	journal	September 1988
Size-consistent Brueckner theory limited to double substitutions Handy, Nicholas C.; Pople, John A.; Head-Gordon, Martin Chemical Physics Letters, Vol. 164, Issue 2-3 https://doi.org/10.1016/0009-2614(89)85013-4	journal	December 1989
Bound states of a many-particle system Coester, F. Nuclear Physics, Vol. 7 https://doi.org/10.1016/0029-5582(58)90280-3	journal	June 1958
Stability conditions and nuclear rotations in the Hartree-Fock theory Thouless, D. J. Nuclear Physics, Vol. 21 https://doi.org/10.1016/0029-5582(60)90048-1	journal	November 1960
Short-range correlations in nuclear wave functions Coester, F.; Kümmel, H. Nuclear Physics, Vol. 17 https://doi.org/10.1016/0029-5582(60)90140-1	journal	June 1960
Exact eigenstates of the pairing-force Hamiltonian Richardson, R. W.; Sherman, N. Nuclear Physics, Vol. 52 https://doi.org/10.1016/0029-5582(64)90687-X	journal	March 1964
A restricted class of exact eigenstates of the pairing-force Hamiltonian Richardson, R. W. Physics Letters, Vol. 3, Issue 6 https://doi.org/10.1016/0031-9163(63)90259-2	journal	February 1963
Many-fermion theory in expS- (or coupled cluster) form Kümmel, H.; Lührmann, K. H.; Zabolitzky, J. G. Physics Reports, Vol. 36, Issue 1 https://doi.org/10.1016/0370-1573(78)90081-9	journal	February 1978
The solution of the three-particle Bethe-Faddeev equation for finite nuclei Zabolitzky, J. G. Nuclear Physics A, Vol. 228, Issue 2 https://doi.org/10.1016/0375-9474(74)90433-3	journal	August 1974
Theory of the effective interaction in nuclei Zabolitzky, John G.; Ey, W. Nuclear Physics A, Vol. 328, Issue 1-2 https://doi.org/10.1016/0375-9474(79)90236-7	journal	October 1979
Negative parity states in 16O from coupled-cluster equations Emrich, K.; Zabolitzky, J. G. Nuclear Physics A, Vol. 351, Issue 3 https://doi.org/10.1016/0375-9474(81)90181-0	journal	January 1981
Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories Hergert, H.; Roth, R. Physics Letters B, Vol. 682, Issue 1 https://doi.org/10.1016/j.physletb.2009.10.100	journal	November 2009
Ab initio path to heavy nuclei Binder, Sven; Langhammer, Joachim; Calci, Angelo Physics Letters B, Vol. 736 https://doi.org/10.1016/j.physletb.2014.07.010	journal	September 2014
Chiral effective field theory and nuclear forces Machleidt, R.; Entem, D. R. Physics Reports, Vol. 503, Issue 1 https://doi.org/10.1016/j.physrep.2011.02.001	journal	June 2011
Self-consistent Green's function method for nuclei and nuclear matter Dickhoff, W. H.; Barbieri, C. Progress in Particle and Nuclear Physics, Vol. 52, Issue 2 https://doi.org/10.1016/j.ppnp.2004.02.038	journal	April 2004
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Three-nucleon forces in exotic open-shell isotopes Somà, V.; Barbieri, C.; Cipollone, A. EPJ Web of Conferences, Vol. 66 https://doi.org/10.1051/epjconf/20146602005	journal	January 2014
Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian Piecuch, Piotr; Włoch, Marta The Journal of Chemical Physics, Vol. 123, Issue 22 https://doi.org/10.1063/1.2137318	journal	December 2005
Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces Taube, Andrew G.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 128, Issue 4 https://doi.org/10.1063/1.2830236	journal	January 2008
Multireference coupled-cluster theory: The easy way Musiał, Monika; Perera, Ajith; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 134, Issue 11 https://doi.org/10.1063/1.3567115	journal	March 2011
Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations Jeziorski, B.; Paldus, J. The Journal of Chemical Physics, Vol. 88, Issue 9 https://doi.org/10.1063/1.454528	journal	May 1988
Doubly electron-attached and doubly ionized equation-of-motion coupled-cluster methods with 4-particle–2-hole and 4-hole–2-particle excitations and their active-space extensions Shen, Jun; Piecuch, Piotr The Journal of Chemical Physics, Vol. 138, Issue 19 https://doi.org/10.1063/1.4803883	journal	May 2013
Quasiparticle Fock-space coupled-cluster theory Stolarczyk, Leszek Z.; Monkhorst, Hendrik J. Molecular Physics, Vol. 108, Issue 21-23 https://doi.org/10.1080/00268976.2010.518981	journal	November 2010
Coupled-cluster calculations for ground and excited states of closed- and open-shell nuclei using methods of quantum chemistry Włoch, Marta; Gour, Jeffrey R.; Piecuch, Piotr Journal of Physics G: Nuclear and Particle Physics, Vol. 31, Issue 8 https://doi.org/10.1088/0954-3899/31/8/007	journal	July 2005
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum Duguet, T. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2 https://doi.org/10.1088/0954-3899/42/2/025107	journal	December 2014
Infrared extrapolations for atomic nuclei Furnstahl, R. J.; Hagen, G.; Papenbrock, T. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3 https://doi.org/10.1088/0954-3899/42/3/034032	journal	February 2015
The Ame2012 atomic mass evaluation Wang, M.; Audi, G.; Wapstra, A. H. Chinese Physics C, Vol. 36, Issue 12 https://doi.org/10.1088/1674-1137/36/12/003	journal	December 2012
Electron correlations in the Bogoljubov coupled-cluster formalism Emrich, K.; Zabolitzky, J. G. Physical Review B, Vol. 30, Issue 4 https://doi.org/10.1103/PhysRevB.30.2049	journal	August 1984
Translationally invariant coupled cluster theory for simple finite systems Bishop, R. F.; Flynn, M. F.; Boscá, M. C. Physical Review C, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevC.42.1341	journal	October 1990
Faddeev description of two-hole–one-particle motion and the single-particle spectral function Barbieri, C.; Dickhoff, W. H. Physical Review C, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevC.63.034313	journal	February 2001
Faddeev treatment of long-range correlations and the one-hole spectral function of 16 O Barbieri, C.; Dickhoff, W. H. Physical Review C, Vol. 65, Issue 6 https://doi.org/10.1103/PhysRevC.65.064313	journal	June 2002
Coupled-cluster approach to nuclear physics Dean, D. J.; Hjorth-Jensen, M. Physical Review C, Vol. 69, Issue 5 https://doi.org/10.1103/PhysRevC.69.054320	journal	May 2004
Coupled-cluster calculations for valence systems around O 16 Gour, J. R.; Piecuch, P.; Hjorth-Jensen, M. Physical Review C, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevC.74.024310	journal	August 2006
Coupled-cluster theory for three-body Hamiltonians Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review C, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevC.76.034302	journal	September 2007
New analysis method of the halo phenomenon in finite many-fermion systems: First applications to medium-mass atomic nuclei Rotival, V.; Duguet, T. Physical Review C, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevC.79.054308	journal	May 2009
Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions Hagen, G.; Papenbrock, T.; Dean, D. J. Physical Review C, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevC.82.034330	journal	September 2010
Toward open-shell nuclei with coupled-cluster theory Jansen, G. R.; Hjorth-Jensen, M.; Hagen, G. Physical Review C, Vol. 83, Issue 5 https://doi.org/10.1103/PhysRevC.83.054306	journal	May 2011
Microscopic self-energy calculations and dispersive optical-model potentials Waldecker, S. J.; Barbieri, C.; Dickhoff, W. H. Physical Review C, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevC.84.034616	journal	September 2011
Ab initio self-consistent Gorkov-Green's function calculations of semimagic nuclei: Formalism at second order with a two-nucleon interaction Somà, V.; Duguet, T.; Barbieri, C. Physical Review C, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevC.84.064317	journal	December 2011
Ab initio Gorkov-Green's function calculations of open-shell nuclei Somà, V.; Barbieri, C.; Duguet, T. Physical Review C, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevC.87.011303	journal	January 2013
Ab initio calculations of medium-mass nuclei with explicit chiral 3 N interactions Binder, Sven; Langhammer, Joachim; Calci, Angelo Physical Review C, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevC.87.021303	journal	February 2013
In-medium similarity renormalization group with chiral two- plus three-nucleon interactions Hergert, H.; Bogner, S. K.; Binder, S. Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.034307	journal	March 2013
Spherical coupled-cluster theory for open-shell nuclei Jansen, G. R. Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.024305	journal	August 2013
Extension of coupled-cluster theory with a noniterative treatment of connected triply excited clusters to three-body Hamiltonians Binder, Sven; Piecuch, Piotr; Calci, Angelo Physical Review C, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevC.88.054319	journal	November 2013
Self-consistent Green's functions formalism with three-body interactions Carbone, Arianna; Cipollone, Andrea; Barbieri, Carlo Physical Review C, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevC.88.054326	journal	November 2013
Systematic expansion for infrared oscillator basis extrapolations Furnstahl, R. J.; More, S. N.; Papenbrock, T. Physical Review C, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevC.89.044301	journal	April 2014
Quasiparticle coupled cluster theory for pairing interactions Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, Jorge Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054305	journal	May 2014
Chiral two- and three-nucleon forces along medium-mass isotope chains Somà, V.; Cipollone, A.; Barbieri, C. Physical Review C, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevC.89.061301	journal	June 2014
In-Medium Similarity Renormalization Group For Nuclei Tsukiyama, K.; Bogner, S. K.; Schwenk, A. Physical Review Letters, Vol. 106, Issue 22 https://doi.org/10.1103/PhysRevLett.106.222502	journal	June 2011
Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order Ekström, A.; Baardsen, G.; Forssén, C. Physical Review Letters, Vol. 110, Issue 19 https://doi.org/10.1103/PhysRevLett.110.192502	journal	May 2013
Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two-Plus-Three-Nucleon Interactions Hergert, H.; Binder, S.; Calci, A. Physical Review Letters, Vol. 110, Issue 24 https://doi.org/10.1103/PhysRevLett.110.242501	journal	June 2013
Isotopic Chains Around Oxygen from Evolved Chiral Two- and Three-Nucleon Interactions Cipollone, A.; Barbieri, C.; Navrátil, P. Physical Review Letters, Vol. 111, Issue 6 https://doi.org/10.1103/PhysRevLett.111.062501	journal	August 2013
Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group Bogner, S. K.; Hergert, H.; Holt, J. D. Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.142501	journal	October 2014
Ab Initio Coupled-Cluster Effective Interactions for the Shell Model: Application to Neutron-Rich Oxygen and Carbon Isotopes Jansen, G. R.; Engel, J.; Hagen, G. Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.142502	journal	October 2014
Coupled Cluster Calculations of Ground and Excited States of Nuclei Kowalski, K.; Dean, D. J.; Hjorth-Jensen, M. Physical Review Letters, Vol. 92, Issue 13 https://doi.org/10.1103/PhysRevLett.92.132501	journal	April 2004
Ab-Initio Coupled-Cluster Study of O 16 Włoch, M.; Dean, D. J.; Gour, J. R. Physical Review Letters, Vol. 94, Issue 21 https://doi.org/10.1103/PhysRevLett.94.212501	journal	June 2005
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/RevModPhys.79.291	journal	February 2007
Modern theory of nuclear forces Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G. Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1773	journal	December 2009
Colloquium : Three-body forces: From cold atoms to nuclei Hammer, Hans-Werner; Nogga, Andreas; Schwenk, Achim Reviews of Modern Physics, Vol. 85, Issue 1 https://doi.org/10.1103/RevModPhys.85.197	journal	January 2013
E FFECTIVE F IELD T HEORY FOR F EW -N UCLEON S YSTEMS Bedaque, Paulo F.; van Kolck, Ubirajara Annual Review of Nuclear and Particle Science, Vol. 52, Issue 1 https://doi.org/10.1146/annurev.nucl.52.050102.090637	journal	December 2002

Cited By (16)

Emergent properties of nuclei from ab initio coupled-cluster calculations Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. Physica Scripta, Vol. 91, Issue 6 https://doi.org/10.1088/0031-8949/91/6/063006	journal	May 2016
Symmetry broken and restored coupled-cluster theory: II. Global gauge symmetry and particle number Duguet, T.; Signoracci, A. Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 1 https://doi.org/10.1088/0954-3899/44/1/015103	journal	December 2016
Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer Dallaire-Demers, Pierre-Luc; Romero, Jonathan; Veis, Libor Quantum Science and Technology, Vol. 4, Issue 4 https://doi.org/10.1088/2058-9565/ab3951	journal	September 2019
Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain Cipollone, A.; Barbieri, C.; Navrátil, P. Physical Review C, Vol. 92, Issue 1 https://doi.org/10.1103/physrevc.92.014306	journal	July 2015
Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians Stroberg, S. R.; Hergert, H.; Holt, J. D. Physical Review C, Vol. 93, Issue 5 https://doi.org/10.1103/physrevc.93.051301	journal	May 2016
Neutron matter from chiral two- and three-nucleon calculations up to N 3 LO Drischler, C.; Carbone, A.; Hebeler, K. Physical Review C, Vol. 94, Issue 5 https://doi.org/10.1103/physrevc.94.054307	journal	November 2016
Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian Ripoche, J.; Lacroix, D.; Gambacurta, D. Physical Review C, Vol. 95, Issue 1 https://doi.org/10.1103/physrevc.95.014326	journal	January 2017
Toward a systematic strategy for defining power counting in the construction of the energy density functional Yang, C. -J.; Grasso, M.; Lacroix, D. Physical Review C, Vol. 96, Issue 3 https://doi.org/10.1103/physrevc.96.034318	journal	September 2017
Radii and Binding Energies in Oxygen Isotopes: A Challenge for Nuclear Forces Lapoux, V.; Somà, V.; Barbieri, C. Physical Review Letters, Vol. 117, Issue 5 https://doi.org/10.1103/physrevlett.117.052501	journal	July 2016
Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques Tichai, A.; Ripoche, J.; Duguet, T. The European Physical Journal A, Vol. 55, Issue 6 https://doi.org/10.1140/epja/i2019-12758-6	journal	June 2019
Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain Cipollone, A.; Barbieri, C.; Navrátil, P. arXiv https://doi.org/10.48550/arxiv.1412.0491	text	January 2014
Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians Stroberg, S. R.; Hergert, H.; Holt, J. D. arXiv https://doi.org/10.48550/arxiv.1511.02802	text	January 2015
Symmetry broken and restored coupled-cluster theory. II. Global gauge symmetry and particle number Duguet, T.; Signoracci, A. arXiv https://doi.org/10.48550/arxiv.1512.02878	preprint	January 2015
Emergent properties of nuclei from ab initio coupled-cluster calculations Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. arXiv https://doi.org/10.48550/arxiv.1601.08203	text	January 2016
Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian Ripoche, J.; Lacroix, D.; Gambacurta, D. arXiv https://doi.org/10.48550/arxiv.1610.04063	text	January 2016
Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques Tichai, Alexander; Ripoche, Julien; Duguet, Thomas arXiv https://doi.org/10.48550/arxiv.1902.09043	text	January 2019

Similar Records

Spherical coupled-cluster theory for open-shell nuclei

Journal Article · Sun Aug 04 20:00:00 EDT 2013 · Physical Review C, Nuclear Physics · OSTI ID:1565057

Structure and dynamics of open-shell nuclei from spherical coupled-cluster theory

Journal Article · Wed Jul 16 20:00:00 EDT 2025 · Physical Review. C · OSTI ID:2573220

From closed shells to open shells: Coupled-cluster calculations of atomic nuclei

Journal Article · Mon Mar 09 20:00:00 EDT 2026 · Physical Review C · OSTI ID:3024320

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Citation Formats

References (60)

Cited By (16)

Similar Records

Related Subjects