Bootstrapping entanglement in quantum spin chains

Jiaju Zhang, Arash Jafarizadeh, M. A. Rajabpour

Published 2023-10-25Version 1

This paper aims to redefine how we understand and calculate the properties of quantum many-body systems, specifically focusing on entanglement in quantum spin systems. Traditional approaches necessitate the diagonalization of the system's Hamiltonian to ascertain properties such as eigenvalues, correlation functions, and quantum entanglement. In contrast, we employ the bootstrap method, a technique that leverages consistency relations rather than direct diagonalization, to estimate these properties. Our work extends the bootstrap approach to quantum spin systems, concentrating on the well-known Lipkin-Meshkov-Glick model with both transverse and longitudinal external magnetic fields. Unlike previous studies that have focused mainly on ground-state properties, our methodology allows for the calculation of a broad range of properties, including energy spectrum, angular momentum, concurrence, tangle, residual tangle, and quantum Fisher information (QFI), for all eigenstates. We show that this approach offers not only a new computational methodology but also a comprehensive view of both bipartite and multipartite entanglement properties across the entire spectrum of eigenstates. Specifically, we demonstrate that states typically found in the central region of the spectrum exhibit greater multipartite entanglement, as indicated by larger QFI values, compared to states at the edges of the spectrum. In contrast, concurrence displays the opposite trend. This observed behavior is in line with the monogamy principle governing quantum entanglement.