近日，韩国光州科学技术院的Keun-Young Kim及其研究团队取得一项新进展。经过不懈努力，他们从可积性到混沌揭示了量子自旋链中的扩展和谱复杂性。相关研究成果已于2024年8月30日在国际知名学术期刊《高能物理杂志》上发表。
该研究团队探究了在量子系统中扩散复杂度和谱复杂度的特性，这些系统展现出从可积性到混沌的过渡，即混合场伊辛模型和海森堡XXZ自旋链的次近邻变形。研究人员证实了扩散复杂度在达到饱和之前出现峰值是混沌系统的一个特征。研究发现，通常情况下，峰值后扩散复杂度的饱和值不仅取决于哈密顿量的谱统计特性，还取决于特定状态。
然而，似乎存在一个由哈密顿量的对称性和维度决定的最大通用界限，该界限在无限温度下的热场双态（TFD）中得以实现。研究人员还发现，扩散复杂度和谱形状因子改变其行为的时间尺度是相互一致的，并且与系统的混沌特性无关。
在谱复杂度的情况下，研究人员确定决定其在混沌系统中饱和值和时间尺度的关键因素，是理论谱中的最小能量差。这解释了文献中关于混沌系统相比其可积性对应系统，更早达到饱和的观察结果。最后，研究人员讨论了TFD的性质，他们推测这些性质使其适合用于探测量子多体系统中的混沌特征。
附：英文原文
Title: Spread and spectral complexity in quantum spin chains: from integrability to chaos
Author: Camargo, Hugo A., Huh, Kyoung-Bum, Jahnke, Viktor, Jeong, Hyun-Sik, Kim, Keun-Young, Nishida, Mitsuhiro
Issue&Volume: 2024-08-30
Abstract: We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We corroborate the observation that the presence of a peak in spread complexity before its saturation, is a characteristic feature in chaotic systems. We find that, in general, the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. However, there appears to be a maximal universal bound determined by the symmetries and dimension of the Hamiltonian, which is realized by the thermofield double state (TFD) at infinite temperature. We also find that the time scales at which the spread complexity and spectral form factor change their behaviour agree with each other and are independent of the chaotic properties of the systems. In the case of spectral complexity, we identify that the key factor determining its saturation value and timescale in chaotic systems is given by minimum energy difference in the theory’s spectrum. This explains observations made in the literature regarding its earlier saturation in chaotic systems compared to their integrable counterparts. We conclude by discussing the properties of the TFD which, we conjecture, make it suitable for probing signatures of chaos in quantum many-body systems.
DOI: 10.1007/JHEP08(2024)241
Source: https://link.springer.com/article/10.1007/JHEP08(2024)241