Phase space analysis of the 3-level Lipkin-Meshkov-Glick model using parity adapted U(D)-spin coherent states

• Published in: Journal of physics. Conference series Vol. 2667; no. 1; pp. 12065 - 12072
• Main Authors: Mayorgas, A, Guerrero, J, Calixto, M
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2023
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/2667/1/012065

Abstract We study the phase-space properties of the 3-level Lipkin-Meshkov-Glick as paradigmatic case of critical, parity symmetric, N -quDit systems undergoing a quantum phase transition in the thermodynamic limit N → ∞ . We generalize U(2) spin coherent states to U( D ) (quDits), and define the coherent state representation Q ψ (Husimi function) of a symmetric N - quDit state |ψ〉 in the phase space ℂ P D −1 = U( D ) / [U(1) × U( D − 1)]. This allows us to define parity adapted U(D) coherent states ( -DCATs), which reproduce accurately the lowest energy Hamiltonian eigenstates obtained by numerical diagonalization. We visualize precursors of the QPTs by plotting localization measures (Husimi function and its moments) of the parity adapted U(D) coherent states and the numerical Hamiltonian eigenstates for a finite number of particles.