论文标题
探索基态能的交叉导数探索量子相变
Exploring quantum phase transitions by the cross derivative of the ground state energy
论文作者
论文摘要
在这项工作中，Gibbs自由能的交叉衍生物最初是针对经典自旋模型中的相变的[Phys。 Rev. B 101，165123（2020）]扩展到量子系统。我们以各向异性为例以SPIN-1 XXZ链为例，以证明其对高斯型量子相变的有效性和便利性。这些高阶过渡对于通过常规方法确定非常具有挑战性。从相对于两个各向异性强度的交叉导数中，每个系统大小都可以清楚地观察到一个山谷结构。山谷深度的有限大小外推显示了完美的对数差异，这表明了相变的发作。同时，相关长度的临界点和临界指数是通过每个大小的山谷位置的幂律拟合来获得的。结果与文献中的最佳估计非常一致。还简要讨论了其在具有连续相变的其他量子系统中的应用。
In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models [Phys. Rev. B 101, 165123 (2020)], is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.
