微扰共形场论的能级分布
Energy Level Distribution of Perturbed Conformal Field Theories
摘要：
我们研究了有限体积中扰动共形极小模型的能级间距，考虑了这种模型的扰动是大规模的，但不一定可积。我们用改进的重整化群截断共形谱方法计算了它们的谱。用这种方法，我们能够研究超过40000个状态被保存的系统，我们确定的最低的几千个本征态的能量与高精度。我们发现，正如预期的那样，可积微扰极小模型的能级间距统计是泊松的，而不可积微扰的统计是GOE样的。然而，通过改变系统的大小（从而控制理论在其IR和UV极限之间的定位），可以引起两个统计分布之间的交叉。
英文摘要：
We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group improved truncated conformal spectrum approach. With this method we are able to study systems where more than 40000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy. We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of non-integrable perturbations are GOE-like. However by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions.
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