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    题名: 找尋混亂量子系統中的量子糾纏(I)
    作者: 林瑜琤
    Lin, Yu-Cheng
    贡献者: 國立政治大學應用物理研究所
    行政院國家科學委員會
    关键词: 物理
    日期: 2009
    上传时间: 2012-11-07 14:53:46 (UTC+8)
    摘要: 量子糾纏是量子力學的最基本特徵，且是量子計算不可獲缺的資源。 瞭解量子多體系統裡的量子糾纏度是目前一跨越各研究領域的挑戰。 不具沮喪性的自旋1/2 反鐵磁海森堡模型之基態可被視為價鍵態的疊加。 其價鍵結構與量子糾纏有著緊密的關聯性。利用一特殊的量子蒙地卡羅 的計算方法我們得以精確地研究海森堡模型的基態特性, 包含其價鍵糾纏熵。 我們提出一新的糾纏熵量度，並以大尺度的量子蒙地卡羅計算驗證 二維海森堡模型的Neel基態糾纏熵遵循所謂的“表面積定律“。
    Entanglement is one of the most fundamental features of quantum mechanics, and is a key resource for quantum computation. Understanding the degree of entanglement of quantum many-body systems is currently one of the most challenging problems connecting many disciplines. The ground state of an unfrustrated S=1/2 Heisenberg antiferromagnet can be viewed as a superposition of valence-bond states. The valence-bond structure is closely related to quantum entanglement. Ground state properties, including the valence-bond entanglement entropy, can be studied without approximations using projector quantum Monte Carlo (QMC) simulations. We investigate definitions of entanglement entropy based on individual valence bonds connecting two subsystems, as well as shared loops of the transposition graph (overlap) of two valence-bond states. We reformulate a previously used definition based on valance bonds in the wave function as a true ground state expectation value, and find that its scaling for the Heisenberg chain agrees with an exact result. The loop-based entanglement entropy of the two-dimensional Heisenberg model is shown to satisfy the area law with an additive logarithmic correction, unlike single-bond definitions, which exhibit multiplicative logarithmic corrections.
    關聯: 基礎研究
    學術補助
    研究期間:9810~9907
    研究經費:1526仟元
    数据类型: report
    显示于类别:[應用物理研究所 ] 國科會研究計畫

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