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Constant of Motion Identifying Excited-State Quantum Phases
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-09-24 , DOI: 10.1103/physrevlett.127.130602
Ángel L Corps 1 , Armando Relaño 1
Affiliation  

We propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator C^, which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues ±1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, C^ explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law.

中文翻译:

识别激发态量子相位的运动常数

我们提出一大类激发态量子相变 (ESQPT) 会产生两种不同的激发态量子相。这些阶段由操作员识别C^,这只是其中一个的运动常数。因此,ESQPT 临界能量将光谱分成一个阶段,其中物理可观测值的平衡期望值关键取决于此运动常数,而另一个阶段则能量是唯一相关的热力学量级。这个算子的商标特征是它有两个不同的特征值±1,因此,它在这两个阶段的第一个阶段充当离散对称。在具有和不具有附加离散对称性的系统中都可以观察到这种情况;在第一种情况下,C^解释了越过临界线时从简并双峰到非简并本征能级的变化。我们在 Rabi 和 Dicke 模型中提供了严格的数值证据,表明该结果在热力学极限中是准确的,有限大小的修正随着幂律而减小。
更新日期:2021-09-24
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