Quantum Fisher information in one-dimensional translation-invariant quantum systems: Large-N limit analysis

Abstract

The large-N limit is a crucial property in many-body quantum systems, playing a important role in advancing quantum theories and technologies. This paper explores the large-N limit of quantum Fisher information (QFI), an experimentally accessible quantum information measure, in one-dimensional (1D) translation-invariant quantum systems. We demonstrate that QFI generally scales as ${\varrho }_2{N}^2+{\varrho }_{1}N$ in the large-N limit for these systems. Notably, we present a method to extract the scaling coefficients $\left\{{\varrho }_i\right\}$ using triangular-matrix-product-operator theory and infinite tensor-network algorithms, circumventing the need for finite-size scaling fittings. By analyzing ground states in infinite-size transverse-field Ising chains and cluster chains, we reveal that $\left\{{\varrho }_i\right\}$ offer a concise and informative approach to characterize the achievable precision limit in parameter estimations, metrologically useful multipartite entanglement, quantum criticality, and their relationship in these systems in the large-N limit.