DUKELSKY , Jorge

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 that can be diagonalized for large number of bosons. We present results for the low-energy spectrum and the...

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We...

We introduce the basic concepts of catastrophe theory needed to derive analytically the phase diagram of the proton–neutron interacting boson model (IBM-2). Previous studies [1–3] were based on numerical solutions. We here explain the whole IBM-2 phase diagram including the precise order of the phase transitions in terms of the cusp catastrophe .

We study the phase diagram of the proton-neutron interacting boson model 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.

We present a new and consistent mapping of colorless three-quark clusters onto colorless triplet fermions (baryons) and test it in the context of a three-color extension of the Lipkin model. For systems with two triplets (for which the problem can be solved without approximation both before and after the mapping), we exactly reproduce the...

The Bose-Hubbard model coupled to a Feshbach resonance is studied. Quantum phase transitions are analyzed within a beyond mean field framework in order to get finite size corrections to the simple mean field approach. Analytical results for the ground state energy and the first few energy gaps are presented.

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The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of...

We introduce a simple two-level boson model with the same energy surface as the Q-consistent interacting boson model Hamiltonian. The model can be diagonalized for large number of bosons and the results used to check analytical finite-size corrections to the energy gap and the order parameter in the critical region.

Background: The Agassi model [D. Agassi, Nucl. Phys. A 116, 49 (1968)NUPABL0375-947410.1016/0375-9474(68)90482-X] is an extension of the Lipkin-Meshkov-Glick (LMG) model [H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965)NUPHA70029-558210.1016/0029-5582(65)90862-X] that incorporates the pairing interaction. It is a schematic...

The Agassi model (Agassi 1968 Nucl. Phys. A 116 49) is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick model (Lipkin et al 1965 Nucl. Phys. 62 188). In this paper we review the algebraic formulation of an extension of the Agassi model as...

An intrinsic-state formalism for the interacting boson model IBM-4 is presented. A basis of deformed bosons is introduced which allows the construction of a general trial wave function that has Wigner's spin-isospin SU(4) symmetry as a particular limit. Intrinsic-state calculations are compared with exact ones, showing good agreement.

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...

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...

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes...

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...

The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff...

In this work we explore the relationship between an excited state quantum phase transition (ESQPT) and the phenomenon of quantum decoherence. For this purpose, we study how the decoherence is affected by the presence of a continuous ESQPT in the environment. This one is modeled as a two level boson system described by a Lipkin Hamiltonian. We...

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes...

We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited...

A Hartree-Bose mean-field approximation for the IBM-3 is presented. A Hartree-Bose transformation from spherical to deformed bosons with charge-dependent parameters is proposed which allows bosonic pair correlations and includes higher angular momentum bosons. The formalism contains previously proposed IBM-2 and IBM-3 intrinsic states as...

A Hartree-Bose mean-field approximation for the IBM-3 is presented. A Hartree-Bose transformation from the spherical to the deformed bosons with charge-dependent parameters is proposed which allows bosonic pair correlations and includes higher angular momentum bosons. The formalism contains previously proposed IBM-2 and IBM-3 intrinsic states...

We study the similarities and differences between the phenomena of Quantum Decoherence and Quantum Quench in presence of an Excited State Quantum Phase Transition (ESQPT). We analyze, on one hand, the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics and, on the other, we...

In this contribution, the critical behavior of excited state quantum phase transitions (ESQPT's) and its relation to order and chaos in the Dicke model are studied. This model is nonintegrable. For comparison, the same problem is studied for the Jaynes-Cummings model which is, somehow, the integrable version of the Dicke model. The existence of...