Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation

Santos L.F. Tavora M. Pérez-Bernal F.
Physical Review A
Doi 10.1103/PhysRevA.94.012113
Volumen 94
Citas: 23
© 2016 American Physical Society.Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-12 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.
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