Interacting spin waves in quantum antiferromagnetsin two dimensions.

这个项目建立在动量空间中非微扰连续相似变换(CSTs)方法学的最新进展的基础上，这使得我们能够定量地理解聚合正方形晶格Heisenberg模型的磁激发及其动力学关联。CST将强关联量子多体问题映射到一个有效的模型，该模型守恒具有强相互吸引相互作用的修饰自旋波的数量。在这里，我们将这一方法扩展到两个方向：首先，我们考虑了正方形晶格海森堡模型的无阻变形，例如易轴XXZ模型、双层正方形晶格海森伯格模型和所谓的J-Q模型，从而可以通过修饰的自旋波和Higgs振幅模的光谱特性来研究长程Neel有序的量子临界击穿。其次，我们在正方形格子海森堡模型中增加了几何挫折感。具体地说，我们重点研究了正方形晶格上的J1-J2模型和空间各向异性的三角形晶格。在这两种情况下，在磁有序相中，大部分Brillioun区的自旋波的衰变和束缚态的形成都是可以预料的。对这些现象的描述需要对本项目中发展的CST方案进行修改，该方案允许我们对这些受挫量子磁体中从磁有序状态到势能量子自旋液体的量子相变有新的见解。

This project builds on the recent methodological progress fornon-perturbative continuous similarity transformations (CSTs) in momentum space,which enables a quantitative understanding of the magnetic excitations and their dynamic correlations of the paradigmatic square-lattice Heisenberg model. The CST maps the strongly correlated quantum many-body problem to an effective model conserving the number of dressed spin waves with strong mutual attractive interactions. Here we extend this approach in two directions: First, we consider unfrustrated deformations of the square-lattice Heisenberg model such as the easy-axis XXZ model, the bilayer square-lattice Heisenberg model, and the so-called J-Q-model, so that the quantum-critical breakdown of the long-range Neel order can be investigated via the spectral properties of dressed spin waves and of the Higgs amplitude modes. Second, we add geometric frustration to the square-lattice Heisenberg model. Specifically, we focus on the J1-J2-model on the square lattice and on the spatially anisotropic triangular lattice. In both cases, the decay of spin waves in large parts of the Brillioun zone and the formation of bound states state is expectedin the magnetically ordered phases. The description of these phenomena requiresmodifications of the CST scheme which is developed in this project and which allows us to gain novel insight into the quantum phase transitions fromthe magnetically ordered state to the potential quantum spin liquids in these frustrated quantum magnets.