Calculating properties of the Fermi-Hubbard model using advanced numerical techniques

摘要：我正在进行的项目旨在使用最新的数值技术来计算费米-哈伯德模型的各种性质。我们使用的基于图解的算法对于模型的某个参数范围是最好的，这是一个特别重要的参数范围，因为这是当前使用超冷气体进行的量子模拟实验所达到的范围。评估该算法的技术涉及到使用图解蒙特卡罗数值计算计算的数据来寻找相关可观测对象在某些参数中的级数展开。我要做的是开发使用这些信息来计算感兴趣的质量的方法，要么直接从系列中计算，要么使用更复杂的技术间接找到更多信息。该项目的新内容是进一步提高了场的能力，以准确地计算具有受控误差棒的许多电子系统的性质。该项目可能最终试图扩展或改进算法以计算更高阶的级数系数或更奇异的分位数和/或使用当前形式的算法计算实验或数值上感兴趣的量。

Summary: The project I am working on aims to calculate various properties of the Fermi-Hubbard model using the most up to date numerical techniques available. The Diagrammatic based algorithm that we are using is the best available for a certain range of parameters of the model and this is a particularly important range of parameters since it is the range that current quantum simulation experiments using ultracold gases are reaching.The technique for evaluating the involves using data calculated from the diagrammatic monte carlo numerical calculations to find the power series expansion of a relevant observable in some parameter. What I will be doing is developing ways to use this information to calculate qunatities of interest, either directly from the series or using more complex techniques to find more information indirectly. The novel content of the project is the furthering of the capabilities of the field to accurately calculate properties of many electron systems with controlled errorbars. The project may end up attempting to extend or improve upon the algortihm to calculate the series coefficients to higher orders or for more exotic quantites and/or calculating experimentally or numerically interesting quantities using the algorithm in its current form.