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

使用先进的数值技术计算 Fermi-Hubbard 模型的属性

• 批准号: 2125376
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2125376
• 关键词: Calculating; properties; Fermi; Hubbard; model

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.

总结：我正在进行的项目旨在使用最先进的数值技术计算费米-哈伯德模型的各种特性。我们正在使用的基于图解的算法是对模型的一定参数范围的最佳可用算法，这是一个特别重要的参数范围，因为它是当前使用超冷气体的量子模拟实验所达到的范围。利用图解蒙特卡罗数值计算得到的数据，求出某参数下相关观测值的幂级数展开式。我要做的是开发使用这些信息来计算感兴趣的数量的方法，或者直接从序列中，或者使用更复杂的技术来间接地找到更多的信息。该项目的新内容是进一步提高该领域的能力，以精确计算许多具有控制误差的电子系统的性质。项目最终可能会尝试扩展或改进算法，以计算更高阶的级数系数或更奇特的数量和/或使用当前形式的算法计算实验或数值上有趣的数量。