论文标题
旋转链中的复杂性和信息几何形状
Complexity and information geometry in spin chains
论文作者
论文摘要
我们研究了一类可解决的一维自旋系统的尼尔森的复杂性和fubini-study的复杂性。我们的示例包括横向XY自旋链及其自然扩展，即带有外部磁场的量子指南针模型。我们在热力学极限中获得了量子相变附近的两种复杂性的缩放行为，这是系统参数的函数。我们在信息几何框架中提供了这些分析证明，该框架验证了我们的数值分析。还建立了尼尔森复杂性与系统大小的缩放，接近临界。在某些特殊情况下，对于所有模型，我们还获得了Fubini研究复杂性的分析表达式，而在更通用情况下进行数值分析。我们的研究清楚地表明了准无效率系统中两个复杂性概念的差异。
We study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without an external magnetic field. We obtain the scaling behaviour of both complexities near quantum phase transitions in the thermodynamic limit, as a function of the system parameters. We provide analytical proofs of these, in an information geometric framework, which verify our numerical analysis. The scaling of the Nielsen complexity with the system size is also established, close to criticality. We also obtain analytic expressions for the Fubini-Study complexity in some special cases for all the models, while a numerical analysis in more generic situations is carried out. Our study clearly demonstrates the differences in the two notions of complexity in quasi-free fermionic systems.
