AI 中文总结
该研究在Lipkin-Meshkov-Glick模型中，通过引入诱导一阶基态量子相变的项破缺宇称对称，却保留能量二重态的指数简并性，揭示其源于系统经典极限相空间的ℤ₂对称。
AI 中文摘要
量子力学中的简并模式源于系统对称性，著名的Lipkin-Meshkov-Glick（LMG）模型的破缺对称相由具有不同宇称的双重简并态构成。本研究表明，即使宇称不守恒，这类二重态仍可存在。为此，我们以具有二阶基态量子相变（GSQPT）及丰富能谱（含两种不同的激发态量子相变）的非谐LMG哈密顿量为起点，在哈密顿量中引入诱导一阶GSQPT的项，该破缺了宇称对称但保留了能量二重态中的指数简并性。我们证明此现象可追溯至系统经典极限相空间中存在的ℤ₂对称（反射对称），其会在量子系统中导出反幺正的ℤ₂对称。
英文摘要
Degeneracy patterns in quantum mechanics stem from the system symmetries. In particular, the broken-symmetry phase in the well-known Lipkin-Meshkov-Glick (LMG) model is composed of doubly-degenerate states of different parity. In this work, we show that such doublets can exist even if parity is not conserved. For this purpose, our starting point is an anharmonic LMG Hamiltonian with a second-order ground-state quantum phase transition (GSQPT) and a rich spectrum, with two different excited-state quantum phase transitions. The inclusion in the Hamiltonian of a term inducing a first-order GSQPT breaks the parity symmetry but conserving the exponential degeneracy in the energy doublets. We demonstrate that this phenomenon can be traced back to the existence of a $\mathbb{Z}_2$ symmetry (reflection symmetry) in the system's classical limit phase space that leads to an anti-unitary $\mathbb{Z}_2$ symmetry in the quantum system.
