Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level lipkin-meshkov-glick atom models

作     者：Calixto, Manuel Mayorgas, Alberto Guerrero, Julio 

作者机构：Department of Applied Mathematics Institute Carlos I of Theoretical and Computational Physics University of Granada Fuentenueva s/n Granada18071 Spain Department of Mathematics University of Jaen Campus Las Lagunillas s/n Jaen23071 Spain 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2021年

核心收录：

主　　题：Phase transitions 

摘      要：We introduce the notion of Mixed Symmetry Quantum Phase Transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector µ, when some Hamiltonian control parameters λ are varied. We use a three-level Lipkin-Meshkov-Glick (LMG) model, with U(3) dynamical symmetry, to exemplify our construction. After reviewing the construction of U(3) unirreps using Young tableaux and Gelfand basis, we firstly study the case of a finite number N of three-level atoms, showing that some precursors (fidelity-susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasi-classical) states of U(3) as variational states, we compute the lowest-energy density for each sector µ in the thermodynamic N → ∞ limit. Extending the control parameter space by µ, the phase diagram exhibits four distinct quantum phases in the λ-µ plane that coexist at a quadruple point. The ground state of the whole system belongs to the fully symmetric sector µ = 1 and shows a four-fold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat *** Codes 81V45, 81V70, 81R05, 81R30 Copyright © 2021, The Authors. All rights reserved.