近來冷原子在光晶格上的操控技術有了矚目的發展，開啟了實驗物理在強相關統系以及多體現象研究上的一個全新方向。基於這些系統的複雜性和強相關特質，對於解析方法研究是一個重大挑戰。因此量子蒙地卡羅模擬的精準性成為研究光晶格一個不可多得的工具。在這計畫中，我們將會利用量子蒙地卡羅計算去研究強相關玻色子系統，當中包括玻色子混合、玻色子費米子混合和無序玻色子混合等系統，我們對這些系統中可能存在的量子態只有有限的了解，特別是超固體態、玻璃態等異常量子態的存在性，以及它們的特性和相關量子相變都是迫切須要研究的重要課題。 The impressive technological advances in trapping cold atoms in optical lattices have opened a new frontier in the study of strongly correlated systems and make the investigation of many-body phenomena experimentally accessible. While analytical study of most strongly correlated systems is usually very difficult, if not infeasible, quantum Monte Carlo (QMC) simulations are exact and ideally suited for a wide range of models. In this project, we propose to use QMC method to study numerically the strongly correlated bosonic systems, including Bose mixtures, Bose-Fermi mixtures as well as disordered Bose models. Phase diagrams of these systems are not well understood. The possibility of novel phases, such as supersolid state and glassy state, and the nature of the quantum phase transitions are important open questions that needed to be addressed.
