论文标题
临界量子自旋链中kac-moody对称性的出现
Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains
论文作者
论文摘要
给定具有微观群体对称性的临界量子自旋链，例如对于$ u（1）$或$ su（2）$旋转各向同性，我们数字地研究了低能和长距离时Kac-Moody对称性的出现。在该制度中，一种关键的量子自旋链由一个保形场理论描述，即与保守电流相关的kac-moody代数增强了与保守的代数相关的常规virasoro代数。具体而言，我们首先提出了一种构造与Kac-Moody Generators相对应的晶格运算符的方法。然后，我们从数字上表明，当投射到量子自旋链的低能状态上时，这些操作员确实大约满足了Kac-Moody代数。 Kac-Moody Generator的晶格版本使我们能够计算所谓的水平常数，并将晶格哈密顿氏晶格的低能特征性组织到Kac-Moody Towers中。我们使用XXZ模型和海森堡模型以近代邻居耦合来说明该提案。
Given a critical quantum spin chain with a microscopic Lie-group symmetry, corresponding e.g. to $U(1)$ or $SU(2)$ spin isotropy, we numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. In that regime, one such critical quantum spin chain is described by a conformal field theory where the usual Virasoro algebra associated to conformal invariance is augmented with a Kac-Moody algebra associated to conserved currents. Specifically, we first propose a method to construct lattice operators corresponding to the Kac-Moody generators. We then numerically show that, when projected onto low energy states of the quantum spin chain, these operators indeed approximately fulfill the Kac-Moody algebra. The lattice version of the Kac-Moody generators allow us to compute the so-called level constant and to organize the low-energy eigenstates of the lattice Hamiltonian into Kac-Moody towers. We illustrate the proposal with the XXZ model and the Heisenberg model with a next-to-nearest-neighbor coupling.
