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

摘要

Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) to excitedlevels. They are associated with local divergences in the density of states. Here, we investigate how the presence of anESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of theeigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonianwith infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model andthe limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studiesfor the dynamics, we uncover similarities between the LMG and the noninteracting XX models.