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 a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

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 states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

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 through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law. Real quantum systems always interact with the environment. This interaction leads to decoherence, the process by which quantum information is degraded and purely quantum properties of a system are lost. Decoherence provides a theoretical basis for the quantum-classical transition ͓1͔, emerging as a possible explanation of the quantum origin of the classical world. It is also a major obstacle for building a quantum computer ͓2͔ since it can produce the loss of the quantum character of the computer. Therefore a complete characterization of the decoherence process and its relation with the physical properties of the system and the environment is needed for both fundamental and practical purposes.The connection between decoherence and environmental quantum phase transitions has been recently investigated ͓3-5͔. A universal Gaussian decay regime in the fidelity of the system was initially identified, and related to a secondorder quantum phase transition in the environment ͓4͔; as a consequence, the decoherence process was postulated as an indicator of a quantum phase transition in the environment. Subsequently, this analysis was refined, and it was found that the universal regime is neither always Gaussian ͓6͔, nor always related to an environmental quantum phase transition ͓5͔.In this paper we analyze the relationship between decoherence and an environmental excited state quantum phase transition ͑ESQPT͒. We show that the fidelity of a single qubit, coupled to a two-level boson environment, becomes singular when the system-environment coupling energy equals the critical energy for the occurrence of a continuous ESQPT in the environment. Therefore our results establish that a critical phenomenon in the environment entails a singular behavior in the decoherence induced in the central system.An ESQPT is a nonanalytic evolution of some excited states of a system as the Hamiltonian control parameter is varied. It is analogous to a standard quantum phase transition ͑QPT͒, but taking place in some excited state of the system, which defines the critical energy E c at which the transition takes place. We can distinguish between different kinds of ESQPTs. As it is stated in ͓7͔, in the thermodynamic limit a crossing of two levels at E = E c determines a first order ES-QPT, while if the number of interacting levels is locally large at E = E c but without real crossings, the ESQPT is continuous. In th...

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 propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.

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.