Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
arxiv(2023)
Abstract
Excited-state quantum phase transitions (ESQPTs) strongly influence the
spectral properties of collective many-body quantum systems, changing
degeneracy patterns in different quantum phases. Level degeneracies, in turn,
affect the system's dynamics. We analyze the degeneracy dependence on the size
of two-level boson models with a u(n+1) dynamical algebra, where n is the
number of collective degrees of freedom. Below the ESQPT critical energy of
these models, the energy gap between neighboring levels that belong to
different symmetry sectors gets close to zero as the system size increases. We
report and explain why this gap goes to zero exponentially for systems with one
collective degree of freedom, but algebraically in models with more than one
degree of freedom. As a consequence, we show that the infinite-time average of
out-of-time-order correlators is an ESQPT order parameter in finite systems
with n=1, but in systems with n>1, this average only works as an order
parameter in the mean-field limit.
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