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• W2620791113 abstract "Abstract Part I: Quantum Collective Spin Systems We use a coherent spin state formalism in order to study collective spin models, which have many applications in physics. In particular, the Lipkin-Meshkov-Glick (LMG) has been analyzed in the thermodynamic limit. The method developed during this work can, in principle, be used for more general Hamiltonians written as a function of the su(2) algebra generators. We have derived exact expressions for the integrated density of states for this model. The nature of the density of states singularities has been detailed. The first order finite size corrections as well as observables expectation values were also computed. The standard Bohr-Sommerfeld quantization approach, adapted to the spin case, is no longer valid near the spectral singularities. In order to treat these cases, we have developed a new approach that permits to describe the spectrum in the neighbourhood of the critical points. Part II: Adiabatic Quantum Computation We have proposed a simple model which highlights the relations between quantum phase transitions and adiabatic (quantum) computation. This model puts in evidence the importance of the choice of the initial Hamiltonian and of the adiabatic path in the parameter space; it should be helpful as a toy model for more realistic cases. We have also studied the state populations dynamics when a quantum phase transition point is crossed, for the LMG model studied in the first part. Numerical simulations show that the dynamics of the populations is very sensitive to the presence of exceptional points in the spectrum, which a simplified model for the quantum evolution already suggests." @default.
• W2620791113 created "2017-06-09" @default.
• W2620791113 creator A5032268476 @default.
• W2620791113 date "2008-09-12" @default.
• W2620791113 modified "2023-09-24" @default.
• W2620791113 title "Quantum Phase Transitions in Collective Spin Models. Applications to Adiabatic Quantum Computation" @default.
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