标题： 通过时间尺度纠缠诊断相变 显示英文标题

标题： Diagnosing phase transitions through time scale entanglement

摘要： 我们提出了一种新方法，基于将任意多点关联压缩为四维张量链，并研究其所谓的键维度作为系统时间尺度纠缠的指标。这种四维张量链诊断方法使我们能够i)识别量子相变（基态交叉）和热交叉，ii)通过iii)使用任意可用的关联函数和iv)通过改变四维张量链截断来处理低精度输入数据，从而区分这两种情况。我们通过研究哈伯德二聚体的相图、有无最近邻跃迁的四点哈伯德环以及单杂质安德森模型来验证该方法的有效性。我们发现时间尺度纠缠是系统固有的属性，在相变和交叉处达到最大值，这表现为关联函数的四维张量链键维度的峰值。此外，还展示了该方法与其他物理量之间的联系，例如各种纠缠度量和灵敏度。 显示英文摘要

摘要： We propose a new method based on the compression of arbitrary multi-point correlators into quantics tensor trains and studying its so called bond dimension as an indicator of time scale entanglement in the system. This quantics tensor train diagnostics approach allows us to i) identify quantum phase transitions (ground state crossings) and thermal crossovers, ii) distinguish between these two by allowing flexibility through iii) using arbitrary available correlators and iv) the possibility to deal with low-accuracy input data through varying the quantics tensor train cutoffs. We verify the validity of the approach by studying the phase diagram of the Hubbard dimer, the four-site Hubbard ring with and without next-nearest neighbor hopping and the single-impurity Anderson model. We find time scale entanglement to be a system-inherent property becoming maximal at phase transitions and crossover, which translates to peaks in the quantics tensor train bond dimension of correlator functions. Additionally, the connection of the method to other physical quantities, such as various entanglement measures and susceptibilities, is shown.