Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis,Physical Review E

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Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-15 , DOI: 10.1103/physreve.104.034119
Qian Wang ₁ , Francisco Pérez-Bernal ₂

Affiliation

Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.

中文翻译：

量子多体系统中激发态量子相变的特征：相空间分析

使用 Husimi 准概率分布，我们研究了 Lipkin-Meshkov-Glick 和耦合顶部模型中激发态量子相变 (ESQPT) 的相空间特征。我们表明 ESQPT 由 Husimi 函数的动力学证明，在不同的 ESQPT 阶段表现出明显的时间依赖性。我们还讨论了如何从长期平均 Husimi 函数及其相关的边际分布中识别 ESQPT 签名。此外，根据长期平均 Husimi 函数的计算二阶矩和 Wherl 熵，我们估计了两种模型中 ESQPT 的临界点，与分析（平均场）结果非常吻合。我们提供了确凿的证据，证明相空间方法既是检测的新探针，也是研究 ESQPT 的宝贵工具。

更新日期：2021-09-16

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