Symmetry conserving coupled cluster doubles wave function and the self-consistent odd particle number RPA
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Regular Article - Theoretical Physics
Symmetry conserving coupled cluster doubles wave function and the self-consistent odd particle number RPA M. Jemaï1,2,a , P. Schuck3,4,b 1
Laboratory of Advanced Materials and Quantum Phenomena, Physics Department, FST, El-Manar University, 2092 Tunis, Tunisia ISSATM, Carthage University, Avenue de la République, P.O. Box 77, 1054 Amilcar, Tunis, Tunisia 3 Université Paris-Saclay, CNRS-IN2P3, IJCLab, 91405 Orsay Cedex, France 4 Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
2
Received: 4 August 2020 / Accepted: 7 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Vittorio Somà
Abstract Mixing single and triple fermions an exact annihilation operator of the Coupled Cluster Doubles wave function with good symmetry was found in Tohyama and Schuck (Phys Rev C 87:044316, 2013). Using these operators with the equation of motion method the so-called self-consistent odd particle number random phase approximation (oddRPA) was set up. Together with the stationarity condition of the two body density matrix it is shown that the annihilation conditions allow to reduce the order of correlation functions contained in the matrix elements of the odd-RPA equations to a fully self consistent equation for the single particle occupation numbers. Excellent results for the latter and the ground state energies are obtained in an exactly solvable model from weak to strong couplings.
1 Introduction It is well known that the coupled cluster (CC) wave function is a powerful many-body ansatz. In this work we will use an approximation thereof, the so-called coupled cluster doubles (CCD) wave function. It is not easy nor straightforward to perform calculations with the CCD wave function. The technique most in use [2–4] is to project the equations for the ground state energy onto successively more complicated m p-mh configurations with m = 1, 2, . . . and p, h single particle (s.p.) states above and below the Fermi level, respectively. Often excellent results have been obtained with these methods in various fields of physics (nuclear physics, chemistry, condensed matter, etc.) [3,4]. However, the method runs into difficulties when the system under consideration undergoes a transition to a spontaneously broken symmetry. A typical a e-mail:
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example is the transition to superconductivity of electronic systems or to super-fluidity of other Fermi systems like there are nuclear systems or cold atoms in traps. This is particularly relevant for finite systems where considering a definite number of particles can become mandatory. Very recently there have, thus, been attempts to formulate symmetry projected CCD approaches: (i) using BCS quasi-particle basis with projection to good particle number [5] (ii) an effort has also been undertaken for parity projection in the Lipkin model [6] (iii) also spin-projected CC ha
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