Characterizing the Lipkin-Meshkov-Glick excited-state spectrum through the quantum coherence spectrum

Excited-state quantum phase transitions extend the quantum phase transition concept beyond the ground state and offer insights into the complex behavior of quantum systems. In the present work we assess the use of the multiple quantum coherence spectrum as a valid tool to probe excited-state quantum phase transitions within the framework of the Lipkin-Meshkov-Glick model. The time dependence and the long-time average of the multiple quantum coherence spectrum reveal the intricate dynamics that stems from the existence of singularities in the excited-state spectrum of a quantum many-body system.