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

对26年前发现的氧化铜化合物的高温超导性的物理机制的理解，仍然是凝聚态理论研究的一个突出和有价值的目标。事实上，人们普遍认为，现象学中最重要的方面可以用存在于这些材料中的强电子相关性来解释。然而，即使是最简单的强相关电子晶格模型的相图的精确测定，如t-J或Hubbard模型，它们被认为是捕捉高温超导体的基本物理，到目前为止，即使是最复杂的现有分析和数值计算工具，也被证明是一项任务。事实上，关于t-J和哈伯德模型是否具有超导基态，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中相分离的发生，仍在激烈争论中。这项研究工作的目的是利用一种非常有前途的，最近引入的方法，被称为纠缠斑块变分蒙特卡罗（EPVMC），试图为有关t-J或哈伯德模型的低温特性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方法已被证明在“受挫”磁系统的研究中是有效的，即强相关的电子模型，这些模型以前没有得到令人满意的理论分析。因此，它似乎为上述强相关电子模型的研究提供了一条可能的途径。由于EPVMC的应用需要将其扩展和推广到一半以下的电子填补情况（特别是流动空缺的情况），因此这项拟议的工作也可能具有重要的方法发展方面。

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.