Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

Abstract

Using the Wherl entropy, we study the delocalization in phase-space of energy eigenstates in the vicinity of avoided crossing in the Lipkin-Meshkov-Glick model. These avoided crossing, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase space regions, which contrary to the low energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wherl entropy is observed for eigenstates close to the critical energy of the excited-state quantum phase transition (ESQPT). This allows to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi functions of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.

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• Excited-state quantum phase transitions
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• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model
• Relaxation time as a control parameter for exploring dynamical phase diagrams
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• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• Exact solutions and Dynamical phase transitions in the Lipkin-Meshkov-Glick model with Dual nonlinear interactions
• Quantum signatures and semiclassical limitations in the transmission of Fock states
• Energy cat states induced by a parity-breaking excited-state quantum phase transition