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Excited state quantum phase transitions in collective many-body quantumsystems influence the system spectral properties due to changing degeneracypatterns in different phases. We report a fundamental difference in the natureof the degeneracy for boson two-level models, depending on the dimension of thespace where the models were defined. To illustrate the consequences, we assessthe validity of an out-of-time-order correlator as a possible order operatorfor excited state quantum phase transitions in different models.

Degeneracy in excited state quantum phase transitions of two-level bosonic models and its influence on system dynamics