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J. Dukelsky

Publications and source records attributed to J. Dukelsky.

At least 55 records · Page 3Linked to original sources
arXiv2006

Two-level interacting boson models beyond the mean field

The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.

nucl-th↗
arXiv2006

Integrable models for asymmetric Fermi superfluids: Emergence of a new exotic pairing phase

We introduce an exactly-solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on an equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair-excitations. It is proven that this phase is the exact ground state in the strong coupling limit, while numerical examples demonstrate that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.

cond-mat.other↗
arXiv2006

Exactly-solvable models of proton and neutron interacting bosons

We describe a class of exactly-solvable models of interacting bosons based on the algebra SO(3,2). Each copy of the algebra represents a system of neutron and proton bosons in a given bosonic level interacting via a pairing interaction. The model that includes s and d bosons is a specific realization of the IBM2, restricted to the transition regime between vibrational and gamma-soft nuclei. By including additional copies of the algebra, we can generate proton-neutron boson models involving other boson degrees of freedom, while still maintaining exact solvability. In each of these models, we can study not only the states of maximal symmetry, but also those of mixed symmetry, albeit still in the vibrational to gamma-soft transition regime. Furthermore, in each of these models we can study some features of F-spin symmetry breaking. We report systematic calculations as a function of the pairing strength for models based on s, d, and g bosons and on s, d, and f bosons. The formalism of exactly-solvable models based on the SO(3,2) algebra is not limited to systems of proton and neutron bosons, however, but can also be applied to other scenarios that involve two species of interacting bosons.

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arXiv2006

What is a Cooper pair ?

Recently, the nature of Cooper pairs in the BCS-BEC crossover has regained attention due to the observation of a large fraction of preformed fermion pairs on the BCS side of the Feshbach resonance in ultracold atomic Fermi gases. While several theoretical explanations were proposed, the interpretations are still controversial. The root of the controversy is understanding what represents a Cooper pair in a correlated Fermi system. This paper discusses these issues at the most elementary level.

cond-mat.supr-con↗
arXiv2006

Density matrix renormalization group approach for many-body open quantum systems

The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels. It is shown that the DMRG technique applied to broad resonances in the unbound neutron-rich nucleus 7He provides a highly accurate treatment of the coupling to the non-resonant scattering continuum.

nucl-th↗
arXiv2006

Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

The complete exact solution of the T=1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with non-degenerate single-particle levels and including isospin-symmetry breaking terms. The power of the method is illustrated with a numerical calculation for $^{64}$Ge for a $pf+g_{9/2}$ model space which is out of reach of modern shell-model codes.

nucl-th↗
arXiv2006

Continuous unitary transformations in two-level boson systems

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a 1/N expansion for different observables is proposed and allows one to compute the finite-size scaling exponents at the critical point. Analytical and numerical results are compared and reveal the power of the present approach to compute the finite-size corrections in such a context.

cond-mat.stat-mech↗
arXiv2005

Finite-size scaling exponents in the interacting boson model

We investigate the finite-size scaling exponents for the critical point at the shape phase transition from U(5) (spherical) to O(6) (deformed $γ$-unstable) dynamical symmetries of the Interacting Boson Model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading order correction to the ground state energy, the gap, the expectation value of the $d$-boson number in the ground state and the $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scaling exponents.

cond-mat.stat-mech↗
arXiv2005

The $β^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model

Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a $β^4$ potential.

nucl-th↗
arXiv2005

Boson-Fermion pairing in a Boson-Fermion environment

Propagation of a Boson-Fermion (B-F) pair in a B-F environment is considered. The possibility of formation of stable strongly correlated B-F pairs, embedded in the continuum, is pointed out. The new Fermi gas of correlated B-F pairs shows a strongly modified Fermi surface. The interaction between like particles is neglected in this exploratory study. Various physical situations where our new pairing mechanism could be of importance are invoked.

cond-mat.other↗
arXiv2004

Phase Diagram of the Proton-Neutron Interacting Boson Model

We study the phase diagram of the proton--neutron interacting boson model (IBM--2) with special emphasis on the phase transitions leading to triaxial phases. The existence of a new critical point between spherical and triaxial shapes is reported.

nucl-th↗
arXiv2004

Exactly-Solvable Models Derived from a Generalized Gaudin Algebra

We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Bardeen-Cooper-Schrieffer, Suhl-Matthias-Walker, the Lipkin-Meshkov-Glick, generalized Dicke, the Nuclear Interacting Boson Model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet.

cond-mat.supr-con↗
arXiv2004

Exactly-solvable models for atom-molecule hamiltonians

We present a family of exactly-solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasi-spins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. Application to a system of bosonic atoms and molecules is reported.

cond-mat.soft↗
arXiv2004

Generalized Richardson-Gaudin Nuclear Models

The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie algebra. As an example, the $so(5)\sim sp(4)$ model of T=1 pairing is discussed and illustrated for the case of $^{64}$Ge with non-degenerate single-particle energies.

nucl-th↗
arXiv2004

Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians

Using a new class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest neighbor level spacings. However, these Hamiltonians involve many-body interactions and the addition of a small integrable perturbation very quickly leads the system to a Poisson distribution. Besides this exceptional cases, we show that the accumulated distribution of an ensemble of random integrable two-body pairing hamiltonians is in perfect agreement with the Poisson limit. These numerical results for quantum integrable Hamiltonians provide a further empirical confirmation to the work of the Berry and Tabor in the semiclassical limit.

nlin.CD↗
arXiv2004

Exactly solvable Richardson-Gaudin models for many-body quantum systems

The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the physics of systems with strong pair correlations is reviewed. We begin with a brief discussion of Richardson's early work, which demonstrated the exact solvability of the pure pairing model, and then show how that work has evolved recently into a much richer class of exactly-solvable models. We then show how the Richardson solution leads naturally to an exact analogy between such quantum models and classical electrostatic problems in two dimensions. This is then used to demonstrate formally how BCS theory emerges as the large-N limit of the pure pairing Hamiltonian and is followed by several applications to problems of relevance to condensed matter physics, nuclear physics and the physics of confined systems. Some of the interesting effects that are discussed in the context of these exactly-solvable models include: (1) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains, (2) the role of the nucleon Pauli principle in suppressing the effects of high spin bosons in interacting boson models of nuclei, and (3) the possibility of fragmentation in confined boson systems. Interesting insight is also provided into the origin of the superconducting phase transition both in two-dimensional electronic systems and in atomic nuclei, based on the electrostatic image of the corresponding exactly-solvable quantum pairing models.

nucl-th↗
arXiv2004

Self Consistent Random Phase Approximation and the restoration of symmetries within the three-level Lipkin model

We show that it is possible to restore the symmetry associated with the Goldstone mode within the Self Consistent Random Phase Approximation (SCRPA) applied to the three-level Lipkin model. We determine one and two-body densities as very convergent expansions in terms of the generators of the RPA basis. We show that SCRPA excitations correspond to the heads of some rotational bands in the exact spectrum. It turns out that the SCRPA eigenmodes for N=2 coincide with exact solutions, given by the diagonalisation procedure.

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