$O(3)$ 与解禁闭量子临界点处的 Lee-Yang 零点
Lee-Yang zeros at $O(3)$ and deconfined quantum critical points
AI总结：
提出一种统计精确的大规模量子 Monte Carlo 方法计算复值外场下的配分函数零点，并成功应用于 2D 量子反铁磁体提取临界指数及观察零点环。
摘要：
Lee-Yang 理论基于对配分函数零点的研究，被广泛认为是研究临界现象的一种强大且互补的方法，并构成了相变理论的基础部分。然而，它的广泛应用因需要引入复值场而变得复杂，这给许多数值方法造成了障碍，特别是在量子情形下，一维以上的研究非常有限。在此，我们提出了一种简单且统计精确的方法，用于在大规模量子 Monte Carlo 模拟背景下计算具有一般复值外场的配分函数零点。我们通过从具有复交错场的 2D 量子反铁磁体的主导 Lee-Yang 零点中提取临界指数来展示这种方法的能力，重点关注 Heisenberg 双层和方格 $J$-$Q$ 模型。该方法还允许我们引入与 valence bond solid 序耦合的复场，在具有纯虚交错场和 valence bond solid 场的 $J$-$Q$ 模型中，我们观察到了扩展的零点环。
英文摘要：
Lee-Yang theory, based on the study of zeros of the partition function, is widely regarded as a powerful and complimentary approach to the study of critical phenomena and forms a foundational part of the theory of phase transitions. Its widespread use, however, is complicated by the fact that it requires introducing complex-valued fields that create an obstacle for many numerical methods, especially in the quantum case where very limited studies exist beyond one dimension. Here we present a simple and statistically exact method to compute partition function zeros with general complex-valued external fields in the context of large-scale quantum Monte Carlo simulations. We demonstrate the power of this approach by extracting critical exponents from the leading Lee-Yang zeros of 2D quantum antiferromagnets with a complex staggered field, focusing on the Heisenberg bilayer and square-lattice $J$-$Q$ models. The method also allows us to introduce a complex field that couples to valence bond solid order, where we observe extended rings of zeros in the $J$-$Q$ model with purely imaginary staggered and valence bond solid fields.
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