标题： (1+1)维O(3)非线性σ模型在有无有限化学势下的张量重正化群研究 显示英文标题

标题： Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

摘要： 我们使用具有无限键维数极限的张量重正定组方法研究(1+1)维O(3)非线性σ模型$D_{\rm cut}\rightarrow \infty$。在化学势为零$\mu=0$的情况下，我们研究了冯·诺依曼和Rényi类型的纠缠熵。通过熵的渐近缩放性质确定中心电荷为$c=1.97(9)$。我们还检查了两种熵之间的一致性。在有限密度区域$\mu\ne 0$，在这个模型中标准蒙特卡罗方法会遇到符号问题，我们研究了量子相变的特性。我们从热力学极限下数密度的$\mu$依赖关系确定了相变点$\mu_{\rm c}$和关联长度的临界指数$\nu$。 动态临界指数$z$也是从时间关联长度随$\mu$的变化而产生的标度行为中提取的。 这是首次成功使用TRG方法计算动态临界指数。 显示英文摘要

摘要： We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension $D_{\rm cut}\rightarrow \infty$. At the vanishing chemical potential $\mu=0$, we investigate the von Neumann and R\'enyi types of entanglement entropies. The central charge is determined to be $c=1.97(9)$ by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with $\mu\ne 0$, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point $\mu_{\rm c}$ and the critical exponent of the correlation length $\nu$ from the $\mu$ dependence of the number density in the thermodynamic limit. The dynamical critical exponent $z$ is also extracted from the scaling behavior of the temporal correlation length as a function of $\mu$. This is the first successful calculation of the dynamical critical exponent with the TRG method.