Interacting spin waves in quantum antiferromagnetsin two dimensions.

本项目建立在动量空间中的非微扰连续相似变换（CST）的最新方法学进展的基础上，这使得能够定量地理解范式正方格子海森堡模型的磁激发及其动力学相关性。CST将强关联量子多体问题映射到一个有效的模型，该模型保持了具有强相互吸引作用的自旋波的数量。在这里，我们扩展这种方法在两个方向：首先，我们考虑的正方形晶格海森堡模型，如易轴XXZ模型，双层正方形晶格海森堡模型，和所谓的J-Q模型的未阻挫变形，使量子临界崩溃的长程Neel秩序可以调查通过的频谱特性的自旋波和希格斯振幅模式。其次，我们在正方格子海森堡模型中加入几何阻挫。具体来说，我们专注于J1-J2模型的正方形晶格和空间各向异性的三角形晶格。在这两种情况下，自旋波在Brillioun区的大部分衰减和束缚态的形成预计在磁有序相。对这些现象的描述需要对CST方案进行修改，CST方案使我们能够对这些受抑量子磁体中从磁有序态到潜在量子自旋液体的量子相变有新的认识。

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.