用熵面积定律的破坏精确确定量子临界点
Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
摘要：
有限尺寸标度分析是计算二维经典统计力学模型和一维量子哈密顿量的相图和临界性质的有力工具。最常用的方法来定位量子临界点是所谓的交叉方法，其中通过比较两种不同晶格尺寸的质量间隙来获得估计。这种方法的成功是由于它的简单性和提供准确结果的能力，即使考虑相对较小的晶格尺寸。在本文中，我们介绍了一个估计，定位量子临界点，通过探索临界和非临界系统中的纠缠熵的已知的不同行为。作为一个基准测试，我们使用这个新的估计来定位量子伊辛链的临界点和自旋为1的Blume-Capel量子链的临界线。最后一个模型的三临界点也得到了。并与标准交叉法进行了比较。我们提出的方法是简单的实施在实践中，特别是在密度矩阵重整化群计算，并提供给我们，像交叉方法，非常小的晶格尺寸，令人惊讶的准确结果。我们的应用表明，所提出的方法有几个优点，与标准的交叉方法相比，我们相信它会成为流行的在未来的数值研究。
英文摘要：
Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.
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