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Precise determination of quantum critical points by the violation of the entropic area law

机译：违反熵区定律精确确定量子临界点

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摘要

Finite-size scaling analysis turns out ttf 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 noncritical 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.
机译：有限尺寸缩放分析证明ttf是计算一维二维相位统计图和量子哈密顿力学模型和量子哈密顿量的重要工具。定位量子临界点最常用的方法是所谓的交叉方法，该方法通过比较两个不同晶格尺寸的质量间隙来获得估计值。该方法的成功是由于其简单性以及即使考虑相对较小的晶格尺寸也能够提供准确结果的能力。在本文中，我们介绍了一种估计器，该估计器通过探索临界和非临界系统中纠缠熵的已知不同行为来定位量子临界点。作为基准测试，我们使用这个新的估算器来定位量子伊辛链的临界点和自旋1 Blume-Capel量子链的临界线。最后一个模型的三临界点也已获得。还介绍了与标准穿越方法的比较。我们提出的方法在实践中很容易实现，特别是在密度矩阵重归一化组计算中，并且像交叉方法一样，为我们提供了非常小的晶格大小的惊人准确结果。我们的应用表明，与标准交叉方法相比，该方法具有许多优点，并且我们相信它将在未来的数值研究中变得流行。

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