论文标题
2D Lorentzian Quantum regge微积分的张量网络方法
Tensor network approach to 2d Lorentzian quantum Regge calculus
论文作者
论文摘要
我们证明了量子lorentzian Quantum regge conculus（QRC）的张量重新归一化组（TRG）计算。通过离散简单歧管的连续边缘长度并将其识别为张量指数，以张量网络表示该模型。通过高阶TRG方法获得的时空面积的期望值很好地再现了确切的值。 Lorentzian模型没有峰值配置，这是欧几里得QRC中的障碍物，但它仍然具有长度差的配置，称为捏合几何形状。我们发现，通过检查简单数量较大的限制的平均边缘长度平方，可以抑制捏合几何形状。这意味着Lorentzian模型可以描述平滑的几何形状，尽管需要对较高矩的调查才能使该陈述更加结论。我们的结果还表明，TRG是对简单量子重力的数值研究的有前途的方法。
We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries, although the investigation of the higher moments is required to make the statement more conclusive. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.
