Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review C

Test of many-body methods on an exactly soluble model with backbending and gapless superconductivity

S. Y. Chu, Eugene R. Marshalek, Peter A. Ring, Joachim Krumlinde, John O Rasmussen

Published Sep 1, 1975• 15 citations
Publisher

Abstract

The exactly soluble R(8) model of Krumlinde and Szyma\ifmmode \acute{n}\else \'{n}\fi{}ski is used as a testing ground for three many-body methods applied to the yrast band: (i) the self-consistent cranking model, (ii) self-consistent cranking plus random-phase approximation, and (iii) variation after projection of particle number. All three methods agree very well with exact results outside of the critical region. The behavior in the critical region is examined in detail.NUCLEAR STRUCTURE Many-body methods, solvable model, high-spin states.

DOI
10.1103/physrevc.12.1017

Related papers

Phase transitions in exactly soluble models

Guillermo H. Bozzolo, J. Núñez, Angelo Plastino

A linearized version of the Hartree-Fock method is reinvestigated in order to develop a new technique for the study of phase transitions. This is studied with reference to an exactly soluble model, yielding excellent results.NUCLEAR STRUCTURE Phase transitions. Approximate many body methods applied to a soluble model.

Physical Review C•Dec 1, 1982•4 citations

Study of nuclear structure by using many-body theory

Nguyễn Quang Hưng

Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.

•Jan 1, 2011•0 citations

Comparing many-body approaches against the helium atom exact solution

Jing Li, N. D. Drummond, Peter Schuck +1 more

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

arXiv:1801.09977•SciPost Physics•Apr 1, 2019•22 citations

Coherent correlated pair method versus Hartree-Fock with a soluble SU(3) Hamiltonian

A. Klar, Frank James Margetan, James P. Vary +1 more

We test the coherent correlated pair method with the soluble SU(3) Hamiltonian of Li, Klein, and Dreizler. We compare the results for the ground state energy with the exact solution and with the Hartree-Fock results as a function of coupling parameters and number of particles. For all cases the coherent correlated pair method yields the better upper bound to the ground state energy.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bounds to ground state energies; applications to exactly soluble SU(3) $N$-fermion model.

Physical Review C•Dec 1, 1983•5 citations

Comparing many-body approaches against the helium atom exact solution

Jing Li, Drummond, Neil David, Peter Schuck +1 more

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

•Apr 1, 2019•17 citations

Ordinary and Higher Random-Phase Approximations on the Luttinger Model

N. J. Kupelian

The exactly solvable Luttinger model for a system of one-dimensional, massless, two-component fermions interacting via general two-body forces is used as a test case for a systematically generated sequence of decoupling approximations commonly referred to as random-phase approximations (RPA) of which the simple RPA is the lowest. It is found, irrespective of both the nature and strength of the interaction, that the exact (collective) spectrum, as well as the exact correlation energy, can already be obtained in the simple RPA, and furthermore, that the next higher RPA gives a vanishing correction to these quantities. It is also shown, quite in contradistinction to the exact result, that the free-gas momentum distribution ${\overline{n}}_{k}$ persists in the second RPA as well as in the first, thereby eliminating the higher RPA as a possible approach to the calculation of ${\overline{n}}_{k}$. Thus, in the context of this particular model, although the first few orders of RPA are highly effective for calculating the excitation spectrum and correlation energy, they are sensibly powerless in their ability to predict any variation in structure beyond that of the free-gas distribution, a result which most probably holds as well in the realistic three-dimensional case.

Physical Review•Apr 5, 1968•2 citations
The exactly soluble R(8) model of Krumlinde and Szyma\ifmmode \acute{n}\else '{n}\fi{}ski is used as a testing ground for three many-body methods applied to the yrast band: (i) the self-consistent cranking model, (ii) self-consistent cranking plus random-phase approximation, and (iii) variation after projection of particle number. All three methods agree very well with exact results outside of the critical region. The behavior in the critical region is examined in detail.NUCLEAR STRUCTURE Many-body methods, solvable model, high-spin states.
Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
We test the coherent correlated pair method with the soluble SU(3) Hamiltonian of Li, Klein, and Dreizler. We compare the results for the ground state energy with the exact solution and with the Hartree-Fock results as a function of coupling parameters and number of particles. For all cases the coherent correlated pair method yields the better upper bound to the ground state energy.NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bounds to ground state energies; applications to exactly soluble SU(3) NNN-fermion model.
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
The exactly solvable Luttinger model for a system of one-dimensional, massless, two-component fermions interacting via general two-body forces is used as a test case for a systematically generated sequence of decoupling approximations commonly referred to as random-phase approximations (RPA) of which the simple RPA is the lowest. It is found, irrespective of both the nature and strength of the interaction, that the exact (collective) spectrum, as well as the exact correlation energy, can already be obtained in the simple RPA, and furthermore, that the next higher RPA gives a vanishing correction to these quantities. It is also shown, quite in contradistinction to the exact result, that the free-gas momentum distribution n‾k{\overline{n}}_{k}nk​ persists in the second RPA as well as in the first, thereby eliminating the higher RPA as a possible approach to the calculation of n‾k{\overline{n}}_{k}nk​. Thus, in the context of this particular model, although the first few orders of RPA are highly effective for calculating the excitation spectrum and correlation energy, they are sensibly powerless in their ability to predict any variation in structure beyond that of the free-gas distribution, a result which most probably holds as well in the realistic three-dimensional case.