量子临界点附近的偏振振幅
Polarization amplitude near quantum critical points
摘要：
讨论了一维量子自旋系统的极化振幅。特别地，我们基于二维共形场论研究了这些系统的无隙相。极化振幅被定义为扭曲算符的基态平均值，扭曲算符引起大规范变换，将单位量的U（1）通量附加到系统。我们发现，极化振幅下的周期性边界条件是敏感的扰动周围的不动点的重整化群流，而不是不动点本身，即使当扰动是无关的。这种依赖性被编码到相对于系统大小的标度律中。在本文中，我们将展示如何以及为什么极化振幅的标度律编码的重整化群流的信息。此外，我们还证明了在反周期边界条件下的极化振幅完全由不动点决定，这与在周期边界条件下的极化振幅完全由不动点决定相反，并且它清楚地体现了自旋系统在Lieb-Schultz-Mattis定理意义下的非平凡性.
英文摘要：
We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the U(1) flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.
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