Fisher-Hartwig formula, Entanglement and Correlations

本研究项目涉及量子自旋系统精确可解模型的分析研究，特别强调使用Toeplitz矩阵行列式的Fisher-Hartwig公式研究量子自旋链的熵和相关函数。这项工作对量子信息科学中纠缠的测量具有启示意义。项目将：(1)研究统计物理中XXZ自旋链模型中的熵和纠缠；(2)评估临界状态下XXZ模型的空间、时间和温度相关函数；(3)计算XXZ模型在大数极限下密度矩阵谱的渐近性；(4)研究了Affleck， Kennedy， Lieb和Tasaki的相互作用自旋模型中自旋块的密度矩阵；(5)计算模型推广到其他李群的纠缠熵。这个项目是对信息物理学基础的研究。该项目研究量子信息科学的核心概念——纠缠。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，它对国家安全至关重要，是联邦战略利益的一个领域。本项目涉及一种基于量子自旋系统测量的量子计算方法。

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.