通过一维耦合链阵列理解二维量子系统的纠缠熵和谱
Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
摘要：
我们描述了一个研究二维系统的纠缠熵和谱的算法，作为$N$一维链在其连续极限的耦合阵列。利用该算法研究了二维量子伊辛模型（包括无序相和近临界态），证实了纠缠熵的面积律的存在，并证明了在近临界态存在一个加性块标度，即$c_{eff}\log (N)/6$与$c_{eff} \approx 1$ . \textcolor{black} {通过对纠缠谱的研究，我们证明了纠缠能隙标度可以用来检测2D模型的临界点。当短程（面积定律）纠缠占主导地位，我们发现（数值和微扰），这个频谱反映了一个单一的量子伊辛链的能谱。
英文摘要：
We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its disordered phase and near criticality) we confirm the existence of an area law for the entanglement entropy and show that near criticality there is an additive piece scaling as $c_{eff}\log (N)/6$ with $c_{eff} \approx 1$. \textcolor{black}{Studying the entanglement spectrum, we show that entanglement gap scaling can be used to detect the critical point of the 2D model. When short range (area law) entanglement dominates we find (numerically and perturbatively) that this spectrum reflects the energy spectrum of a single quantum Ising chain.
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