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Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects

J. Gamito1, J. Khalouf-Rivera2, J. M. Arias1,3, P. Pérez-Fernández3,4, and F. Pérez-Bernal2,3

  • 1Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
  • 2Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
  • 3Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
  • 4Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain

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Phys. Rev. E 106, 044125 – Published 17 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044125

Abstract

The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.

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Phys. Rev. E 106, 044125– Published 17 October, 2022
  • Received 10 March 2022
  • Revised 20 July 2022
  • Accepted 15 August 2022
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