Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

中文翻译：

---

无限温度下无序自旋链中谱函数的现象学

受精确数值计算在多大程度上符合多体定位相变的存在这一问题的启发，对无序自旋链的研究最近重新引起了人们的兴趣。对于范式随机场海森堡自旋链，当与自旋相互作用强度相比无序相当时，观察到许多有趣的特征。在这里，我们介绍一种现象学理论，可以解释其中的一些特征。该理论基于接近非相互作用极限，其中系统是安德森绝缘体。以自旋不平衡作为可观察的示例，我们证明了与安德森绝缘体的局部运动积分的接近程度决定了可观察在无限温度下的动力学。