量子磁体中硬核玻色子的有限温度线型：一维实验的图解方法
Finite temperature line-shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension
摘要：
量子磁体中的动力学通常可以用玻色子激发服从硬核约束的有效模型来描述。这样的模型可以系统地推导出重整化方案，如连续酉变换或变分方法。即使在没有进一步相互作用的情况下，核心约束也使核心玻色子的动力学变得不平凡。在这里，我们开发了一个系统的图解方法，在有限温度下的硬核玻色子的光谱特性。从膨胀的热激发玻色子的密度在一个系统中的能隙，我们的方法导致的梯形图的总和。从概念上讲，这种方法并不局限于一维，但一维的情况下提供了一个机会，通过比较，通过映射到乔丹-维格纳费米子获得的确切结果来衡量的方法。特别是，我们提出的结果在有限温度下的单粒子光谱函数的热加宽。发现在高温下的线的形状是不对称的，随着温度的升高，分散体的带宽变窄。此外，热激发玻色子的总数计算和比较各种近似和分析结果。因此，引入了一种灵活的方法，该方法也可以应用于更复杂和更高维的模型。
英文摘要：
The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line-shape is found to be asymmetric at elevated temperatures and the band-width of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced which can also be applied to more sophisticated and higher dimensional models.
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