标题： 通过半定规划松弛方法绘制量子自旋系统的相图 显示英文标题

标题： Mapping phase diagrams of quantum spin systems through semidefinite-programming relaxations

摘要： 识别量子相变是凝聚态物理中的一个重要挑战，因为这需要既提供准确结果又能良好扩展系统大小的方法。 在本工作中，我们展示了如何使用弛豫方法来生成一维和二维量子系统的相图。 为此，我们将基态问题的形式化为一个半定规划问题，我们可以高效地解决它。 然后，通过获取不同模型参数下的算子单项式向量，我们根据它们的余弦相似性来识别所有一阶和二阶相变。 此外，我们展示了如何通过限制相应的可观测量自然地捕捉自发对称性破缺。 使用这些方法，我们重现了一维横场伊辛模型和二维受挫双层海森堡模型的相变。 我们还说明了当引入最近邻相互作用时，后者的相图如何变化。 总体而言，我们的工作展示了弛豫方法如何提供一种新的框架来研究和理解量子相变。 显示英文摘要

摘要： Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation methods can be used to generate the phase diagram for one- and two-dimensional quantum systems. To do so, we formulate a relaxed version of the ground-state problem as a semidefinite program, which we can solve efficiently. Then, by taking the resulting vector of operator monomials for different model parameters, we identify all first- and second-order transitions based on their cosine similarity. Furthermore, we show how spontaneous symmetry breaking is naturally captured by bounding the corresponding observable. Using these methods, we reproduce the phase transitions for the one-dimensional transverse field Ising model and the two-dimensional frustrated bilayer Heisenberg model. We also illustrate how the phase diagram of the latter changes when a next-nearest-neighbor interaction is introduced. Overall, our work demonstrates how relaxation methods provide a novel framework for studying and understanding quantum phase transitions.