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arXiv 2102.07832quant-phmath-phmath.MP
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混合排列对称扇区在临界三能级Lipkin-Meshkov-Glick原子模型热力学极限中的作用

Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models

M. Calixto, A. Mayorgas, J. Guerrero

备注：
15 pages, 9 figures
发表信息：
Phys. Rev. E 103, 012116 (2021)
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摘要：

我们引入了混合对称量子相变（MSQPT）的概念，当某些哈密顿控制参数$λ$变化时，在每个置换对称扇区$μ$内的全同粒子系统的最低能量状态性质的变换中引入了奇点。我们使用具有$U(3)$动力学对称性的三能级Lipkin-Meshkov-Glick（LMG）模型来构造。在回顾了利用Young表和Gelfand基构造$U(3)$单重态的基础上，我们首先研究了有限个$N$三能级原子的情况，发现一些前体（极化率、能级布居等）的存在，并在此基础上讨论了它们的性质。的MSQPT出现在所有置换对称扇区中。利用$U(3)$的相干（准经典）态作为变分态，我们计算了在热力学$N\to\infty$极限下每个扇区$μ$的最低能量密度。通过$μ$扩展控制参数空间，相图在$λ$ - $μ$平面中表现出共存于四重点的四个不同的量子相。整个系统的基态属于完全对称的扇形$μ=1$，由于哈密顿量的宇称对称性的自发破缺，表现出四重简并。这种离散对称性的恢复导致四分量薛定谔猫态的形成。

英文摘要：

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 $N\to\infty$ 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 states.

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