Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems

Abstract

The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$ degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to $L=0$ is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a non-trivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.

14 pages, 6 figures

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• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Impact of chaos on precursors of quantum criticality
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Quantum coherence assisted dynamical phase transition
• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates
• Excited-state quantum phase transitions in constrained systems
• Spectral fluctuations in the interacting boson model
• Energy cat states induced by a parity-breaking excited-state quantum phase transition