@article{10272/13056,
year = {2016},
url = {http://hdl.handle.net/10272/13056},
abstract = {Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) 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-1/2 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.},
organization = {LFS and MT were supported by the NSF grant No. DMR-
1147430. FPB was funded by MINECO grant FIS2014- 53448-C2-
2-P and by Spanish Consolider-Ingenio 2010 (CPANCSD2007-
00042). LFS and FPB thank Pedro Perez- Fernandez and Jorge
Dukelsky for discussions, as well as the hospitality of Alejandro
Frank and the Centro de Ciencias de la Complejidad (C3) at the
UNAM in Mexico, where part of this work was carried out.},
publisher = {American Physical Society},
title = {Excited-state quantum phase transitions in many-body systems with infinite-range interaction : localization, dynamics, and bifurcation},
doi = {10.1103/PhysRevA.94.012113},
author = {Santos, Lea F. and Távora, Marco and Pérez Bernal, Francisco},
}