By analyzing the probability distributions of the Loschmidt echo (LE) and
quantum work, we examine the nonequilibrium effects of a quantum many-body
system, which exhibits an excited-state quantum phase transition (ESQPT).
We find that depending on the value of the controlling parameter the
distribution of the LE displays different patterns.
At the critical point of the ESQPT, both the averaged LE and the averaged
work show a cusplike shape.
Furthermore, by employing the finite-size scaling analysis of the averaged
work, we obtain the critical exponent of the ESQPT.
Finally, we show that at the critical point of ESQPT the eigenstate is a
highly localized state, further highlighting the influence of the ESQPT on the
properties of the many-body system.Comment: 10 pages, 13 figures; accepted for publication in Physical Review
