Truncation effects in the charge representation of the O(2) model
Truncation effects in the charge representation of the O(2) model
复制标题
O(2) 模型的电荷表示中的截断效应
DOI：
10.1103/physrevb.103.245137
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发表时间：
2021
影响因子：
3.7
通讯作者：
Tsai, S.-W.
中科院分区：
文献类型：
--
作者：
Zhang, Jin;Meurice, Y.;Tsai, S.-W.
欧几里德时空中的O（2）模型是紧致标量量子电动力学的零规范耦合极限。我们得到了它的一个对偶表示，称为电荷表示。我们研究的量子相变的电荷表示截断为“自旋”，其中量子数的绝对值小于或等于。电荷表示保留的gapless-to-gapped相变，即使是最小的自旋截断。的相变是一个无限阶的高斯相变，其临界指数和Berezinskiii-Kosterlitz-无边界（BKT）相变相同，而的相变是真的BKT相变。的关联长度的本质奇异性不同于。指数收敛的相变点的拉格朗日和哈密顿公式进行了研究。讨论了用自旋梯算符代替哈密顿量中截断算符的影响。边缘算子在的高斯过渡点处消失，这使得我们能够以高精度提取指数。
The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics. We obtain a dual representation of it called the charge representation. We study the quantum phase transition in the charge representation with a truncation to “spin,” where the quantum numbers have an absolute value less than or equal to. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation. The phase transition foris an infinite-order Gaussian transition with the same critical exponentsandas the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for. The essential singularity in the correlation length foris different from that for. The exponential convergence of the phase-transition point is studied in both Lagrangian and Hamiltonian formulations. We discuss the effects of replacing the truncatedoperators by the spin ladder operatorsin the Hamiltonian. The marginal operators vanish at the Gaussian transition point for, which allows us to extract theexponent with high accuracy.