Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

Localization measures of parity adapted U(D)-spin coherent states applied to the phase space analysis of the D-level Lipkin-Meshkov-Glick model

We study phase space properties of critical, parity symmetric, N-qudit systems undergoing a quantum phase transition (QPT) in the thermodynamic N→∞ limit. The D=3 level (qutrit) Lipkin-Meshkov-Glick model is eventually examined as a particular example. For this purpose, we consider U(D)-spin coherent states (DSCS), generalizing the standard D=2 atomic coherent states, to define the coherent state representation Q_{ψ} (Husimi function) of a symmetric N-qudit state |ψ〉 in the phase space CP^{D-1} (complex projective manifold). DSCS are good variational approximations to the ground state of an N-qudit system, especially in the N→∞ limit, where the discrete parity symmetry Z_{2}^{D-1} is spontaneously broken. For finite N, parity can be restored by projecting DSCS onto 2^{D-1} different parity invariant subspaces, which define generalized "Schrödinger cat states" reproducing quite faithfully low-lying Hamiltonian eigenstates obtained by numerical diagonalization. Precursors of the QPT are then visualized for finite N by plotting the Husimi function of these parity projected DSCS in phase space, together with their Husimi moments and Wehrl entropy, in the neighborhood of the critical points. These are good localization measures and markers of the QPT.

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

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.

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.