Fisher-Hartwig Formula and XY Spin Chain

Fisher-Hartwig 公式和 XY 自旋链

• 批准号: 1205422
• 负责人: Vladimir Korepin
• 金额: $ 25.51万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205422&HistoricalAwards=false
• 关键词: Fisher; Hartwig; Formula; XY; Spin

This award will support a study of entanglement in spin models. In XY spin chains, the entropy of several blocks of spins will be represented as a block Toeplitz determinant, and then the generalized Fisher - Hartwig formula will be used to evaluate asymptotic. The project will consider both von Neumann and Renyi entropies. The entanglement spectrum also will be evaluated. This question has attracted attention recently and requires rigorous mathematical treatment. Entanglement of two blocks of spins in ground states of spin models is important. After tracing the rest of the ground state, these two blocks are left in a mixed state. An appropriate measure of entanglement of mixed systems is negativity. The project will describe entanglement of 2 blocks of spins in the AKLT (Affleck, Lieb, Kennedy Takasi) spin chain by means of negativity. The ground state of the AKLT model is known as valence-bond-solid (VBS) state. It plays an important role in quantum information, especially in measurement based quantum computation.Entanglement is a special phenomenon of quantum systems, which cannot happen in the classical (macroscopic) case. It is an important resource for quantum control, which is central for quantum devices, including quantum computers. This has recently become important, because experimentalist who are working with optical lattices can now build models of interacting spins, which had only previously been studied from the mathematical point of view. This is a substantial contribution of mathematical physics towards the goal of quantum information processing, and progress in the laboratory now depends on further theoretical study. The award will support the mathematical analysis of such entanglement, in order to guide atom-molecular-optics experiments.

该奖项将支持自旋模型中的纠缠研究。在XY自旋链中，几个自旋块的熵将被表示为块Toeplitz行列式，然后使用推广的Fisher - Hartwig公式来计算渐近。该项目将考虑冯诺依曼和Renyi熵。纠缠谱也将被评估。这个问题最近引起了人们的注意，需要严格的数学处理。自旋模型基态中两块自旋的纠缠是很重要的。在追踪基态的其余部分之后，这两个块被留在混合状态。衡量混合系统纠缠度的一个合适的尺度是负性。该项目将通过负性描述AKLT（Affleck，Lieb，Kennedy Takasi）自旋链中2个自旋块的纠缠。AKLT模型的基态被称为价键固体（VBS）态。纠缠是量子系统中的一种特殊现象，在经典（宏观）情况下是不可能发生的。它是量子控制的重要资源，这是量子设备（包括量子计算机）的核心。这一点最近变得很重要，因为研究光学晶格的实验学家现在可以建立相互作用自旋的模型，而以前只从数学角度研究过。这是数学物理学对量子信息处理目标的重大贡献，实验室的进展现在取决于进一步的理论研究。该奖项将支持这种纠缠的数学分析，以指导原子分子光学实验。