Fisher-Hartwig formula, Entanglement and Correlations

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

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.