Fisher-Hartwig formula, Entanglement and Correlations

本研究项目涉及对量子自旋系统精确可解模型的分析研究，特别是利用Toeplitz矩阵行列式的Fisher-Hartwig公式研究量子自旋链的熵和关联函数。这项工作对量子信息科学中的纠缠测量具有重要意义。该项目将：(1)研究统计物理XXZ自旋链模型中的熵和纠缠；(2)在临界区评估XXZ模型中与空间、时间和温度相关的关联函数；(3)计算XXZ模型中密度矩阵谱在大数极限下的渐近性；(4)研究由于Affleck、Kennedy、Lieb和Tasaki相互作用的自旋模型中自旋块的密度矩阵；以及(5)计算推广到其他Lie群的模型中的纠缠熵。本项目是对信息物理学的基础研究。该项目研究纠缠，这是量子信息科学中的一个核心概念。由于量子信息科学在密码学和敏感信息安全传输方面的应用，它对国家安全非常重要，也是联邦战略利益的一个领域。这个项目与一种基于量子自旋系统测量的量子计算方法有关。

This research project concerns analytical investigation of exactly-solvable models of quantum spin systems, with particular emphasis on study of entropy and correlation functions for quantum spin chains using the Fisher-Hartwig formula for the determinant of a Toeplitz matrix. The work has implications for measures of entanglement in quantum information science. The project will: (1) study entropy and entanglement in the XXZ spin chain model of statistical physics; (2) evaluate space-, time- and temperature-dependent correlation functions in the XXZ model in a critical regime; (3) calculate asymptotics for the spectrum of the density matrix in the XXZ model in the large-number limit; (4) study the density matrices of blocks of spins in a model of interacting spins due to Affleck, Kennedy, Lieb and Tasaki; and (5) calculate the entanglement entropy in models generalized to other Lie groups.This project is an investigation of fundamentals in the physics of information. The project studies entanglement, a central concept in quantum information science. Because of its applications to cryptography and secure transmission of sensitive information, quantum information science is important for national security and is an area of federal strategic interest. This project is related to an approach to quantum computation based on measurements in quantum spin systems.