Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Hermes, Matthew R.; Dukelsky, J.; Scuseria, Gustavo E.

doi:10.1103/physrevc.95.064306

Cited by 15 publications

(12 citation statements)

References 42 publications

(95 reference statements)

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“…They derived the phase diagram of the model and the collective excitations in each of the phases by means of HFB and, phRPA and QRPA approximations respectively. More advanced many-body methods like the merging of Coupled Cluster with symmetry restored HFB theory [21] revived the model as an excellent test-bed. Recently, García-Ramos et al [22] generalized the model by the introduction of new interaction terms that give rise to an extremely rich phase diagram.…”

Section: Benchmark With the Agassi Modelmentioning

confidence: 99%

Number conserving particle-hole RPA for superfluid nuclei

et al. 2019

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We present a number conserving particle-hole RPA theory for collective excitations in the transition from normal to superfluid nuclei. The method derives from an RPA theory developed long ago in quantum chemistry using antisymmetric geminal powers, or equivalently number projected HFB states, as reference states. We show within a minimal model of pairing plus monopole interactions that the number conserving particle-hole RPA excitations evolve smoothly across the superfluid phase transition close to the exact results, contrary to particle-hole RPA in the normal phase and quasiparticle RPA in the superfluid phase that require a change of basis at the broken symmetry point. The new formalism can be applied in a straightforward manner to study particle-hole excitations on top of a number projected HFB state.

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Section: Benchmark With the Agassi Modelmentioning

confidence: 99%

Number conserving particle-hole RPA for superfluid nuclei

et al. 2019

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“…9,10 Much of our work in the past year has revolved around combining these two approaches. [11][12][13][14] The main challenge is that the two techniques use fundamentally very different frameworks. Coupled cluster theory introduces a similarity-transformed Hamiltonian constructed via particle-hole excitation operators, and solves this similarity-transformed Hamiltonian in a subspace of the full Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

Qiu

Henderson

Scuseria

2017

The Journal of Chemical Physics

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Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlation but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.

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“…One should note that with the parametrization (13) and (14) and conditions (10), two independent phase selections for u 1 and u −1 are possible: i) u −1 = v 1 = sin β 2 and u 1 = v −1 = cos β 2 , and ii) u −1 = v 1 = sin β 2 and u 1 = −v −1 = − cos β 2 . While the normal density (15) does not depend on the phase selection because the coefficients appear squared, the abnormal density matrix does depend on the phase selected.…”

Section: The Hartree-fock-bogoliuvob Approachmentioning

confidence: 99%

Phase diagram of an extended Agassi model

et al. 2018

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Background: The Agassi model [1] is an extension of the Lipkin-Meshkov-Glick model [2] (LMG) that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960's by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss [3] generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases.Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.

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Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Cited by 15 publications

References 42 publications

Number conserving particle-hole RPA for superfluid nuclei

Number conserving particle-hole RPA for superfluid nuclei

Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

Phase diagram of an extended Agassi model

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