School of Physics and Energy, Shenzhen University, Shenzhen, 518060, China.
School of Physics, Nankai University, Tianjin, 300071, China.
Sci Rep. 2017 Aug 2;7(1):7165. doi: 10.1038/s41598-017-07344-z.
Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 - 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 - 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.
量子相变发生在非厄米系统中。在这项工作中，我们首次表明，密度泛函理论揭示了非厄米多体系统中量子相变和量子纠缠的普遍临界行为。具体来说，我们首先证明，非厄米量子多体系统的非简并定态是定态能量对控制参数导数的普遍函数。这一发现对非厄米系统具有深远的影响。首先，它连接了物理可观测量的非解析行为和定态能量的无解析行为，这解释了为什么非厄米系统中的量子相变发生在有限系统中。其次，它预测了任何物理可观测量在非厄米相变点的普遍标度行为，标度指数为（1-1/p），其中 p 是在例外点处合并态的数量。第三，它揭示了非厄米相变点处的量子纠缠呈现普遍的标度行为，临界指数为（1-1/p）。这些结果揭示了非厄米相变中的普遍临界行为，并为非厄米量子多体物理中纠缠和相变之间提供了深刻的联系。
