Zou Yijian, Milsted Ashley, Vidal Guifre
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phys Rev Lett. 2020 Jan 31;124(4):040604. doi: 10.1103/PhysRevLett.124.040604.
At a quantum critical point, the low-energy physics of a quantum spin chain is described by conformal field theory (CFT). Given the Hamiltonian of a critical spin chain, we propose a variational method to build an approximate lattice representation ϕ_{α} of the corresponding primary CFT operators ϕ_{α}^{CFT}. We then show how to numerically compute the operator product expansion coefficients C_{αβγ}^{CFT} governing the fusion of two primary fields. In this way, we complete the implementation of Cardy's program, outlined in the 1980s, which aims to extract the universality class of a phase transition, as encoded in the so-called conformal data of the underlying CFT, starting from a microscopic description. Our approach, demonstrated here for the critical quantum Ising model, only requires a generic (i.e., in general, nonintegrable) critical lattice Hamiltonian as its input.
在量子临界点，量子自旋链的低能物理由共形场论（CFT）描述。给定一个临界自旋链的哈密顿量，我们提出一种变分方法来构建相应基本CFT算符(\phi_{\alpha}^{CFT})的近似晶格表示(\phi_{\alpha})。然后我们展示如何通过数值计算来得到控制两个基本场融合的算符乘积展开系数(C_{\alpha\beta\gamma}^{CFT})。通过这种方式，我们完成了20世纪80年代概述的卡迪计划的实施，该计划旨在从微观描述出发，提取相变的普适类，这由基础CFT的所谓共形数据编码。我们在此针对临界量子伊辛模型展示的方法仅需要一个一般的（即通常不可积的）临界晶格哈密顿量作为输入。
