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J. Dukelsky

Publications and source records attributed to J. Dukelsky.

At least 19 recordsLinked to original sources
arXiv2021

Variational theory combining number-projected BCS and coupled-cluster doubles

The ground state pairing correlations in finite fermionic systems are described with a high degree of accuracy within a variational approach based on a combined coupled-cluster and particle-number-projected BCS ansatz. The flexibility of this symmetry-preserving wavefunction enables a unified picture valid from weak to strong coupling, both in small and large systems. The present variational approach consistently yields an energy upper bound while operating at the same level of precision of the non-variational particle-number projected Bogoliubov-coupled-cluster theory [Phys. Rev. C 99, 044301 (2019)].

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arXiv2020

Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches

The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among various approaches to include Pauli correlations, in particular, renormalized RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are studied with several cluster approximations for the self-energy of the single-particle Dyson equation. More particle RPA's are shortly discussed with a particular attention to the alpha-particle condensate. Results obtained concerning the Three-level Lipkin, Hubbard and Picket Fence Models, respectively, are outlined. Extended second RPA (ESRPA) is presented.

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arXiv2019

Number conserving particle-hole RPA for superfluid nuclei

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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arXiv2018

Benchmarking the variational reduced density matrix theory in the doubly-occupied configuration interaction space with integrable pairing models

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly-occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.

cond-mat.str-el↗
arXiv2018

Phase diagram of an extended Agassi model

Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick model 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 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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arXiv2016

On the solution of a pairing problem in the continuum

We present a generalized Richardson solution for fermions interacting with the pairing interaction in both discrete and continuum parts of the single particle (s.p.) spectrum. The pairing Hamiltonian is based on the rational Gaudin (RG) model which is formulated in the Berggren ensemble. We show that solutions of the generalized Richardson equations are exact in the two limiting situations: (i) in the pole approximation and (ii) in the s.p. continuum. If the s.p. spectrum contains both discrete and continuum parts, then the generalized Richardson equations provide accurate solutions for the Gamow Shell Model.

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arXiv2016

Structure of the number projected BCS wave function

We study the structure of the number projected BCS (PBCS) wave function in the particle-hole basis, displaying its similarities with coupled clusters theory (CCT). The analysis of PBCS together with several modifications suggested by the CCT wave function is carried out for the exactly solvable Richardson model involving a pure pairing hamiltonian acting in a space of equally-spaced doubly-degenerate levels. We point out the limitations of PBCS to describe the non-superconducting regime and suggest possible avenues for improvement.

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arXiv2015

Advanced density matrix renormalization group method for nuclear structure calculations

We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous $400$ KeV discrepancy in the ground state energy of $^{56}$Ni. We then report the first DMRG results in the $pf+g9/2$ shell model space for the ground $0^+$ and first $2^+$ states of $^{64}$Ge which are benchmarked with reference data obtained from Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of the two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.

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arXiv2012

The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models

The Lipkin-Meshkov-Glick (LMG) model has a Schwinger boson realization in terms of a two-level boson pairing Hamiltonian. Through this realization, it has been shown that the LMG model is a particular case of the SU (1, 1) Richardson-Gaudin (RG) integrable models. We exploit the exact solvability of the model tostudy the behavior of the spectral parameters (pairons) that completely determine the wave function in the different phases, and across the phase transitions. Based on the relation between the Richardson equations and the Lamé differential equations we develop a method to obtain numerically the pairons. The dynamics of pairons in the ground and excited states provides new insights into the first, second and third order phase transitions, as well as into the crossings taking place in the LMG spectrum.

math-ph↗
arXiv2012

Exact solutions for pairing interactions

The exact solution of the BCS pairing Hamiltonian was found by Richardson in 1963. While little attention was paid to this exactly solvable model in the remainder of the 20th century, there was a burst of work at the beginning of this century focusing on its applications in different areas of quantum physics. We review the history of this exact solution and discuss recent developments related to the Richardson-Gaudin class of integrable models, focussing on the role of these various models in nuclear physics.

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arXiv2012

Alpha-like quartet condensation and isovector pairing correlations in N=Z nuclei

We propose a simple quartet condensation model (QCM) which describes with very high accuracy the isovector pairing correlations in self-conjugate nuclei. The quartets have an alpha-like structure and are formed by collective isovector pairs. The accuracy of the QCM is tested for N=Z nuclei for which exact shell model diagonalizations can be performed. The calculations are done with two isovector pairing forces, one extracted from standard shell model interactions and the other of seniority type, acting, respectively, upon spherical and axially-deformed single-particle states. It is shown that for all calculated nuclei the QCM gives very accurate values for the pairing correlations energies, with errors which do not exceed 1%. These results show clearly that the correlations induced by the isovector pairing in self-conjugate nuclei are of quartet type and also indicate that QCM is the proper tool to calculate the isovector proton-neutron correlations in mean field pairing models.

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arXiv2011

Exactly solvable pairing Hamiltonian for heavy nuclei

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the canonical basis.

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arXiv2011

Pairing and alpha-like quartet condensation in N=Z nuclei

We discuss the treatment of isovector pairing by an alpha-like quartet condensate which conserves exactly the particle number, the spin and the isospin. The results show that the quartet condensate describes accurately the isovector pairing correlations in the ground state of systems with an equal number of protons and neutrons

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arXiv2011

Integrable two-channel p_x+ip_y-wave superfluid model

We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the p-wave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact many-body wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition.

cond-mat.quant-gas↗
arXiv2011

Comment on "Fermi-Bose Mixtures near Broad Interspecies Feshbach Resonances"

In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al. introduced a new variational approach to treat strong attractive boson-fermion (BF) correlations in BF atomic mixtures. The proposed theory predicts a first order phase transition to a condensate of composite BF pairs with center of mass momentum Q=0 as opposed to a composite fermionic molecular Fermi gas. We show in this comment that their approach is incorrect and moreover, by resorting to an exactly solvable model we demonstrate that there cannot be more than one correlated Q=0 BF pair in complete contradiction with their conclusions.

cond-mat.quant-gas↗
arXiv2010

Quantum quench influenced by an excited-state phase transition

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear cut evidence of the ESQPT effects is presented in integrable models, while in the nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

quant-ph↗
arXiv2010

Richardson-Gaudin Algebras and the Exact Solutions of the Proton-Neutron Pairing

Many exactly solvable models are based on Lie algebras. The pairing interaction is important in nuclear physics and its exact solution for identical particles in non-degenerate single-particle levels was first given by Richardson in 1963. His solution and its generalization to Richardson-Gaudin quasi-exactly solvable models have attracted the attention of many contemporary researchers and resulted in the exact solution of the isovector pn-pairing within the so(5) RG-model and the equal strength spin-isospin pn-pairing within the so(8) RG-model. Basic properties of the RG-models are summarized and possible applications to nuclear physics are emphasized. MSC2010 Classification: 81U15 Exactly and quasi-solvable systems, 17B81 Applications to physics, 81V35 Nuclear physics, 81R40 Symmetry breaking.

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