Entangled-plaquette Variational Monte Carlo studies of strongly correlated electronic systems

在26年前发现的铜氧化物化合物中，理解高温超导的物理机制仍然是凝聚态理论中一个突出的和有价值的研究目标。事实上，人们普遍认为，现象学最重要的方面可以通过这些材料中存在的强烈电子关联来解释。然而，即使是最简单的强关联电子晶格模型，如被认为捕捉高温超导体基本物理的t-J模型或哈伯德模型，到目前为止，准确确定相图也是一项即使是最复杂的现有分析和数值计算工具也无法完成的任务。事实上，对于t-J和哈伯德模型是否以超导基态为特征，仍然没有达成一致；所有与实验直接相关的重要问题，如条纹的出现或低空穴掺杂时相分离的发生，仍然存在激烈的辩论。 这项研究的目的是利用最近引入的一种非常有前途的方法，称为纠缠斑块变分蒙特卡罗(EPVMC)，试图为关于t-J或Hubbard模型低温性质的最重要的悬而未决的问题提供一个明确的答案，主要是超导基态的可能存在。EPVMC方法已被证明是研究“受挫”磁系统的有效方法，即强关联电子模型，以前一直没有一个令人满意的理论分析。因此，它似乎为上述强关联电子模型的研究提供了一条可能的途径。由于EPVMC的应用需要将其推广和推广到一半以下的电子填报情况(特别是流动空缺的情况)，因此这项拟议工作也有潜在的重要方法学发展方面。

The understanding of the physical mechanism underlying superconductivity at high temperature, in the copper-oxide compounds discovered 26 years ago, remains an outstanding and worthwhile goal of research in condensed matter theory. There is virtually universal agreement that the most important aspects of the phenomenology can be accounted for by strong electronic correlations existing in these materials. However, the accurate determination of the phase diagram of even the simplest lattice models of strongly correlated electrons, such as the t-J or Hubbard model, which are believed to capture the basic physics of high-temperature superconductors, has so far proven a task beyond the capability of even the most sophisticated existing analytical and numerical computational tools. Indeed, there continues to be no agreement as to whether the t-J and Hubbard model feature a superconducting ground state; all-important issues of direct experimental relevance, such as the appearance of stripes or the occurrence of phase separation at low hole doping, are still hotly debated. The purpose of this research effort is to utilize a very promising, recently introduced methodology, known as Entangled-Plaquette Variational Monte Carlo (EPVMC), to attempt to offer a definitive answer to the most important outstanding questions concerning the low temperature properties of the t-J or Hubbard model, chiefly the possible presence of a superconducting ground state. The EPVMC approach has proven effective in the investigation of "frustrated" magnetic systems, i.e., strongly correlated electronic models which had previously eluded a satisfactory theoretical analysis. It seems therefore to offer a possible avenue to the investigation of the above-mentioned strongly correlated electronic models. Because the application of EPVMC requires its extension and generalization to the case of electronic filling below one half (notably to the case of mobile vacancies) there is a potentially significant methodological development aspect to this proposed work as well.