论文标题
标量场理论的双曲线晶格$ _3 $
Hyperbolic Lattice for Scalar Field Theory in AdS$_3$
论文作者
论文摘要
我们通过扩展基于$（2,3,7）$ Triangle群体的Poincaré磁盘上的ADS $ _2 $的等边三角构造来构建ADS $ _3 $的镶嵌，适用于强烈耦合现象和ADS/CFT通讯。提出了有利于研究动力学和量子计算研究的哈密顿式形式。我们显示了自由标量理论的晶格计算和分析结果之间的一致性，并使用蒙特卡洛模拟找到了$ ϕ^4 $理论的二阶临界过渡的证据。讨论了该广告在实时演变和量子计算中的应用程序的应用。
We construct a tessellation of AdS$_3$, by extending the equilateral triangulation of AdS$_2$ on the Poincaré disk based on the $(2,3,7)$ triangle group, suitable for studying strongly coupled phenomena and the AdS/CFT correspondence. A Hamiltonian form conducive to the study of dynamics and quantum computation is presented. We show agreement between lattice calculations and analytic results for the free scalar theory and find evidence of a second order critical transition for $ϕ^4$ theory using Monte Carlo simulations. Applications of this AdS Hamiltonian formulation to real time evolution and quantum computing are discussed.
