Dynamics at and near conformal quantum critical points
Dynamics at and near conformal quantum critical points
复制标题
共形量子临界点及其附近的动力学
DOI：
10.1103/physrevb.83.125114
复制
发表时间：
2010
影响因子：
3.7
通讯作者：
M. Troyer
中科院分区：
文献类型：
--
作者：
S. Isakov;P. Fendley;A. Ludwig;S. Trebst;M. Troyer
我们探索一类特殊的二维量子临界点处及其附近的动力学行为。每个都是共形量子临界点（CQCP），其中在缩放极限内，等时相关器是二维共形场论的相关器。关键理论包括方晶格量子二聚体模型、量子 Lifshitz 理论和变形环面码模型。我们证明，在一般扰动下，后者流向普通洛伦兹不变 (2+1) 维伊辛临界点，说明 CQCP 一般不稳定。我们利用此类系统中经典动力学行为与量子动力学行为之间的对应关系，对量子八顶点模型中的两条 CQCP 线（或等效的两个耦合变形环面码）进行广泛的数值研究。我们发现，沿着 U(1) 对称量子 Lifshitz 线，动力学临界指数保持为 2，而它沿着只有 Z2 对称性的线连续变化。这说明尽管具有相同的等时基态相关器，两个 CQCP 却可以具有截然不同的动力学特性。我们的结果同样适用于相应的纯经典模型的动力学。
We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a two-dimensional conformal field theory. The critical theories include the square-lattice quantum dimer model, the quantum Lifshitz theory, and a deformed toric code model. We show that under generic perturbation the latter flows toward the ordinary Lorentz-invariant (2+1) dimensional Ising critical point, illustrating that CQCPs are generically unstable. We exploit a correspondence between the classical and quantum dynamical behavior in such systems to perform an extensive numerical study of two lines of CQCPs in a quantum eightvertex model, or equivalently, two coupled deformed toric codes. We find that the dynamical critical exponentz remains 2 along theU(1)-symmetric quantum Lifshitz line, while it continuously varies along the line with only Z2 symmetry. This illustrates how two CQCPs can have very different dynamical properties, despite identical equal-time ground-state correlators. Our results equally apply to the dynamics of the corresponding purely classical models.