Beyond mean field study of excited states: Analysis within the Lipkin model

Severyukhin, A. P.; Bender, M.; Heenen, Paul‐Henri

doi:10.1103/physrevc.74.024311

Cited by 16 publications

(15 citation statements)

References 45 publications

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“…As a test case, the Lipkin-Meshkov-Glick (LMG) Model [2,[23][24][25] is considered here. This model consists of N particles distributed in two N-fold degenerated single-particle states separated by an energy ε.…”

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confidence: 99%

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

2012

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Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state fluctuations, are incorporated. In weak coupling, the approach perfectly reproduces the exact quantal dynamics. On the other hand, for increasing coupling strength, above the symmetry breaking threshold, the approach provides description of gross properties (i.e. time averaged behavior) of the exact quantal evolution.

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confidence: 99%

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

2012

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“…In this respect, interested readers can refer to the corresponding discussion in Ref. [44]. Presently, we display results for one representative discretization strategy based on an odd number of equidistant points in the interval ] − π/4, +π/4[.…”

Section: A Set Upmentioning

confidence: 99%

“…The GCM ground-state energy displayed as a function of χ can be found in Ref. [44] for 30 and 50 particles. Consequently, such curves are not reproduced here.…”

Section: A Set Upmentioning

confidence: 99%

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Combining symmetry breaking and restoration with configuration interaction: Extension to z -signature symmetry in the case of the Lipkin model

et al. 2018

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Background: Ab initio many-body methods whose numerical cost scales polynomially with the number of particles have been developed over the past fifteen years to tackle closed-shell mid-mass nuclei. Open-shell nuclei have been further addressed by implementing variants based on the concept of spontaneous symmetry breaking (and restoration). These methods typically access ground states properties and some restricted aspects of spectroscopy.Purpose: In order to access the spectroscopy of open-shell nuclei more systematically while controlling the numerical cost, we design a novel many-body method that combines the merit of breaking and restoring symmetries with those brought about by low-rank individual excitations. Methods:The recently proposed truncated configuration-interaction method based on optimized symmetrybroken and -restored states is extended to the SU (2) group associated with total angular momentum. Dealing more specifically with the Lipkin Hamiltonian, the present study focuses on the breaking and the restoration of the z-signature symmetry associated with a discrete subgroup of SU (2). The highly-truncated N -body Hilbert subspace within which the Hamiltonian is diagonalized is spanned by a z-signature broken and restored Slater determinant vacuum and associated low-rank, e.g. one-particle/one-hole and two-particle/two-hole, excitations. Furthermore, the extent by which the symmetry-unrestricted vacuum breaks z-signature symmetry is optimized in presence of projected low-rank particle-hole excitations. The quality of the method is gauged against exact groundand excited-state eigenenergies for a large range of values of the two-body interaction strength. Furthermore, results are compared to those obtained from the generator coordinate method, the random-phase approximation and the self-consistent (second) random-phase approximation. Results:The proposed method provides an excellent reproduction of the ground-state energy and of low-lying excitation energies of various z-signatures and total angular momenta across the full range of inter-nucleon coupling defining the Lipkin Hamiltonian and driving the normal-to-deformed quantum phase transition. In doing so, the successive benefits of (i) breaking the symmetry, (ii) restoring the symmetry, (iii) including low-rank particlehole excitations and (iv) optimizing the amount by which the underlying vacuum breaks the symmetry are illustrated. While the generator coordinate method building on the same deformed vacua provides results of similar quality, it is not the case of the symmetry-restricted random-phase and self-consistent (second) randomphase approximations in the strongly-interacting regime. Conclusions:The numerical cost of the newly designed variational method is polynomial with respect to the system size. It achieves a good accuracy on the ground-state energy and the low-lying spectroscopy for both weakly-and strongly-interacting systems. The present study confirms the results obtained previously for the attractive pairing Hamiltonian in connection ...

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“…The difference lies mainly in the shaping of interaction which ranges all over the system in the LMG model while nearest neighbor coupling is often used in other realizations. The LMG model has also been used as a test model in a nuclear context [23,24,25,26]. It can be modified to allow for a description of dissipation by allowing a certain spread of excitation energies over the levels [27].…”

Section: Introductionmentioning

confidence: 99%

Stochastic TDHF in an exactly solvable model

et al. 2016

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We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole (2p2h) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of Ω particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small Ω. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow 2p2h transitions. Limitations concerning low energy excitations and memory effects are also discussed.

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Beyond mean field study of excited states: Analysis within the Lipkin model

Cited by 16 publications

References 45 publications

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Combining symmetry breaking and restoration with configuration interaction: Extension to z -signature symmetry in the case of the Lipkin model

Stochastic TDHF in an exactly solvable model

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