Arlei Prestes Tonel

Algebraic properties of an integrable t-J model with impurities

We investigate the algebraic structure of a recently proposed integrable t-J model with impurities, Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading, We prove that the Bethe ansatz states are highest weight vectors of the underlying gl(2\1) supersymmetry algebra, By acting with the gl(2\1) generators we construct a complete set of states for the model

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Emergent quantum phases in a heteronuclear molecular Bose-Einstein condensate model

We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose-Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance

The Two-Site Bose–Hubbard Model

Abstract.The two-site Bose–Hubbard model is a simple model used to study Josephson tunneling between two Bose–Einstein condensates. In this work we give an overview of some mathematical aspects of this model. Using a classical analysis, we study the equations of motion and the level curves of the Hamiltonian. Then, the quantum dynamics of the model is investigated using direct diagonalization of the Hamiltonian. In both of these analyses, the existence of a threshold coupling between a delocalized and a self-trapped phase is evident, in qualitative agreement with experiments.Communicated by Vincent Rivasseau

Thermodynamic properties of an integrable quantum spin ladder with boundary impurities

An integrable quantum spin ladder based on the SU(4) symmetry algebra with boundary defects is studied in the framework of boundary integrability. Five nontrivial solutions of the reflection equations lead to different boundary impurities. In each case the energy spectrum is determined using the quantum inverse scattering method. The thermodynamic properties are investigated by means of the thermodynamic Bethe ansatz. In particular, the susceptibility and the magnetization of the model in the vicinity of the critical points are derived along with differing magnetic properites for antiferromagnetic and ferromagnetic impurity couplings at the edges. The results are applicable to the strong coupling ladder compounds, such as Cu2(C5H12N2)2Cl4.

Integrable Impurity Spin Ladder Systems

Two different types of integrable impurities in a spin ladder system are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly with the Bethe ansatz equations as well as the energy eigenvalues obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. In one of the models the spin gap decreases by increasing the impurity strength A. Moreover, for a fixed A, a reduction in the spin gap by increasing the impurity concentration is also observed.

Classical and quantum analysis of a heterotriatomic molecular Bose-Einstein-condensate model

We investigate an integrable Hamiltonian modeling a heterotriatomic molecular Bose-Einstein condensate. This model describes a mixture of two species of atoms in different proportions, which can combine to form a triatomic molecule. Beginning with a classical analysis, we determine the fixed points of the system. Bifurcations of these points separate the parameter space into different regions. Three distinct scenarios are found, varying with the atomic population imbalance. This result suggests the ground-state properties of the quantum model exhibit a sensitivity on the atomic population imbalance, which is confirmed by a quantum analysis using different approaches, such as the ground-state expectation values, the behavior of the quantum dynamics, the energy gap, and the ground-state fidelity.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter.

Magnetic susceptibility of an exactly solvable anisotropic spin ladder system

We investigate the thermodynamics of an integrable spin ladder model which possesses a free parameter besides rung and leg couplings. The model is exactly solvable by means of the Bethe ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. The spin gap obtained from the susceptibility curve and the one obtained from the Bethe ansatz equations are in very good agreement. Our results for the magnetic susceptibility fit well the experimental data for the organometallic compounds (5IAP)2CuBr4·2H2O (Landee C. P. et al., Phys. Rev. B, 63 (2001) 100402(R)) Cu2(C5H12N2)2Cl4 (Hayward C. A., Poilblanc D. and Levy L. P., Phys. Rev. B, 54 (1996) R12649, Chaboussant G. et al., Phys. Rev. Lett., 19 (1997) 925; Phys. Rev. B, 55 (1997) 3046.) and (C5H12N)2CuBr4 (Watson B. C. et al., Phys. Rev. Lett., 86 (2001) 5168) in the strong-coupling regime.

Integrable spin ladder systems

We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters. We also investigate the thermodynamics of the model. Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically. The influence of this anisotropy parameter on these physical curves is determined explicitly. A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.