Toward an Automated-Algebra Framework for High Orders in the Virial Expansion of Quantum Matter
Toward an Automated-Algebra Framework for High Orders in the Virial Expansion of Quantum Matter
复制标题
DOI：
10.3390/condmat7010013
复制
发表时间：
2021-12
期刊：
影响因子：
1.7
通讯作者：
A. Czejdo;J. Drut;Yaqi Hou;K. J. Morrell
中科院分区：
文献类型：
--
作者：
A. Czejdo;J. Drut;Yaqi Hou;K. J. Morrell
维里展开式为稀态下量子多体系统的热力学提供了非微扰视角。虽然功能强大，但展开式具有挑战性，因为计算每个 n 阶的系数需要分析（如果不能解决）量子 n 体问题。在这项工作中，我们对自动化代数方法进行了全面回顾，我们开发这些方法是为了计算高阶维里系数。这些方法是计算性的但非随机的，从而避免了统计效应；它们在很大程度上也是分析性的，而不是数值性的，并且适合大规模并行计算机架构。我们展示了表征均匀和调和俘获系统的热力学（压力、密度、能量、静态磁化率）的系数的形式和结果，并解释了如何将它们推广到其他可观测量，例如动量分布、Tan接触和结构因子。
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems and explain how to generalize them to other observables such as the momentum distribution, Tan contact, and the structure factor.