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

Abstract

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 systemQ.W. acknowledges support from the Slovenian Research and Innovation Agency under Grants No. J1-4387 and No. P1-0306, National Science Foundation of China under Grant No. 11805165, and Zhejiang Provincial Nature Science Foundation under Grant No. LY20A050001. This project has also received funding from Grant No. PID2022-136228NBC21 funded by MICIU/AEI/10.13039/501100011033 and, as appropriate, by ERDF, A way of making Europe, by ERDF/EU, by the European Union or by the European Union NextGenerationEU/PRTR, and by the FEDER-UHU project POSH-AI, Project No. EPIT1462023. J.K.-R. also acknowledges support from a Spanish Ministerio de Universidades Margarita Salas Fellowship. Computing resources supporting this work were partly provided by the CEAFMC and Universidad de Huelva High Performance Computer located at the Campus Universitario el Carmen and funded by FEDER/MINECO Project No. UNHU-15CE-2848Ciencias Integrada