论文标题
平方晶格上量子Z_2量规理论的真实空间重归化组计算
A real-space renormalization-group calculation for the quantum Z_2 gauge theory on a square lattice
论文作者
论文摘要
我们重新审视弗拉德金（Fradkin）和拉比（Raby）的真实空间重新归一化组方法，用于研究根据形成二维正方形晶格的链接定义的量子z_2规格理论。经过旧的建议，Hirsch和Mazenko开发的系统扰动扩展用于将算法改善算法到二阶偶联，从而结合了丢弃的高能状态的效果。在哈密顿形式主义中提出了对量规不变有效运算符的仔细推导。在非平凡的固定点附近分析了重新归一化组方程，从而在双横向场ISING模型上重申了旧作品。除了恢复HIRSCH先前的发现外，比较了无电（解剖）相中空间相关长度和能量差距的缩放的关键指数。不幸的是，他们的同意很差。基态能量密度的主要奇异行为在临界点附近检查：我们计算一个临界指数并估计临界幅度比率。
We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation expansion developed by Hirsch and Mazenko is used to improve the algorithm to second order in an intercell coupling, thereby incorporating the effects of discarded higher energy states. A careful derivation of gauge-invariant effective operators is presented in the Hamiltonian formalism. Renormalization group equations are analyzed near the nontrivial fixed point, reaffirming old work by Hirsch on the dual transverse field Ising model. In addition to recovering Hirsch's previous findings, critical exponents for the scaling of the spatial correlation length and energy gap in the electric free (deconfined) phase are compared. Unfortunately, their agreement is poor. The leading singular behavior of the ground state energy density is examined near the critical point: we compute both a critical exponent and estimate a critical amplitude ratio.
