具有角$2π$的尖角自由能的对数修正
Logarithmic corrections to the free energy from sharp corners with angle $2π$
摘要：
我们研究了经典二维临界系统中角自由能的次主导修正，重点是由基本的共形场论（CFT）的应力张量引起的一般边界扰动。在一个角度$2π$的特殊情况下，我们发现，有一个不寻常的修正形式$L^{-1}\log L$，其中$L$是一个典型的长度尺度的系统。这种校正也影响角点附近算子的单点函数。前因子可以被看作是半通用的，因为它依赖于一个\emph{single}非通用量，即外推长度。一旦知道了这个紫外截止，这个项就完全由系统的几何形状和CFT的中心荷决定了。例如，在临界状态下的一维量子系统的二分保真度中，就出现了这样一个角落，这使得自由费米子系统中的几个数值检查成为可能。我们还提出了一个确切的结果，在XX和伊辛链，证实了这一分析。最后，我们考虑的应用程序的时间演化的（对数）Loschirst回声和纠缠熵以下的本地量子淬火。由于解析延拓中的微妙问题，我们发现虚时间中的对数项转化为纠缠熵的时间依赖的$L^{-2}$修正，以及Loscherton回波的$L^{-2}\log L$项。
英文摘要：
We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case of an angle $2π$, we find that there is an unusual correction of the form $L^{-1}\log L$, where $L$ is a typical length scale in the system. This correction also affects the one-point function of an operator near the corner. The prefactor can be seen as semi-universal, in the sense that it depends on a \emph{single} non-universal quantity, the extrapolation length. Once this ultraviolet cutoff is known, the term is entirely fixed by the geometry of the system, and the central charge of the CFT. Such a corner appears for example in the bipartite fidelity of a one-dimensional quantum system at criticality, which allows for several numerical checks in free fermions systems. We also present an exact result in the XX and Ising chains that confirms this analysis. Finally, we consider applications to the time evolution of the (logarithmic) Loschmidt echo and the entanglement entropy following a local quantum quench. Due to subtle issues in analytic continuation, we find that the logarithmic term in imaginary time transforms into a time-dependent $L^{-2}$ correction for the entanglement entropy, and a $L^{-2}\log L$ term for the Loschmidt echo.
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