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

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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.