Speaker
Abstract
Effects of excited state quantum phase
transitions over the out-of-time-order
correlators in systems with a U (n) dynamical
algebra
Jamil Khalouf-Rivera, Miguel Carvajal, Francisco P ́erez-Bernal,
Jos ́e Enrique Garc ́ıa-Ramos, Lea F. Santos, Qian Wang
Lie algebras are widely used to study systems in different fields of Physics.
In particular, two levels bosonic models based on unitary algebras U (n) are
used to describe the long-range interaction Ising model as well as molecular
stretching vibrations -U (2)-, molecular bending motion -U (3)-, the rovibra-
tional structure of diatomic molecules -U (4)-, and collective nuclear degrees
of freedom -U (6)-.
In systems with a U (n) dynamical algebra, a model Hamiltonian can
be defined with a single control parameter, which drives the system from
U (n − 1) and to SO(n) dynamical symmetries. It is well known that in
such systems a second order ground state quantum phase transition (QPT)
occurs for a critical value of such control parameter. Moreover, an excited
state QPT appears in the broken-symmetry phase.
In this work, we show that there is a fundamental difference between the
U (2) case and models with U (n) with n ≥ 3. As an application, we compute
the long time limit average of the out-of-time-order correlators in models
with n = 2 and 3.