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

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.

Automated summary

The paper investigates the second-order ground-state quantum phase transition and the excited-state quantum phase transition in the basic Lipkin-Meshkov-Glick model. The inclusion of an anharmonic term leads to a second excited-state quantum phase transition of a different nature. This transition is characterized using the mean field limit of the model, and 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.