2008-08-012024-05-16https://scholars.lib.ntu.edu.tw/handle/123456789/666647摘要：強關聯系統出現許多的奇異量子態，如何將這些態之間的量子相變分類是一個重要研 究的課題。 量子相變的特點是完全因量子漲落的影響而造成量子多體系統基態間急劇 的變化。最近一項從量子資訊科學的新建議：矩陣乘積態(Matrix product state) 是對於 一些量子模型基態的很好的表示方法。對於兩個由相鄰控制參數的有限系統基態間的 量子相變，我們可以利用量子保真度(quantum fidelity)，或重疊模量(overlap modulus) 來表示。我們將開發利用矩陣乘積態的變分蒙特卡羅方法，來研究不同量子模型的基 態，並用這些結果來研究這些奇異態之間的相變。這些課題適合於一個新的科學計算 的模型，稱為圖形處理單元（GPU）計算。我們將開發新的方法和算法，以能在GPU 上進行模擬計算。 其他的研究課題包括具有幾何挫折性的近藤晶格，以及金屬自旋液 體的特性。以上的課題在強關連系統的研究社群具有強烈的興趣，而我們發展的方法 與演算法，對於科學計算社群，也將具有極大的價值。<br> Abstract: Exotic quantum phases emerge in the strongly correlated systems and how one can categorize the quantum phase transitions (QPTs) among these states is an essential issue of research. QPTs are characterized by the drastic change in the ground states of quantum many-body systems, driven solely by quantum fluctuations. Recently, a new proposal from the quantum information science called a matrix product state (MPS) representation are shown to be a useful representation for ground states of several quantum models. The QPT can be indicated by the quantum fidelity, or the overlap modulus, of two finite size ground states with neighboring control parameters. We will develop variational quantum Monte Carlo methods using MPS representation to study ground states of different quantum models, and use this information to study QPTs between these exotic ground states. These problems are suitable for new scientific computation model called graphics processing unit (GPU) computing, and we will develop new methods and algorithms to perform simulations on GPU. Other areas of research including the geometrically frustrated Kondo lattice model and the behavior of the metallic spin liquid. These topics are of fundamental interests of the research community in strongly correlated systems, and methods and algorithms we develop will be of great value to the scientific computation community. 表