Finite-temperature Rydberg atom arrays and energy spectrum computation with tensor networks

Tensor network methods are a family of numerical techniques that efficiently compress the information of quantum many-body systems while accurately capturing their important physical properties. Here, we present a tensor-network-based toolbox developed for constructing the quantum many-body states at thermal equilibrium. Using this framework, we probe classical correlations as well as entanglement monotones of a Rydberg atom array - a promising quantum simulation platform. By examining the entanglement of formation and entanglement negativity of a half-system bipartition, we numerically confirm that a conformal scaling law of entanglement extends from the zero-temperature critical points into the low-temperature regime. Additionally, we explain how our algorithm connects to the excited state search, enabling us to extract the excitation spectrum of a quantum many-body model and offering a new approach in condensed matter studies.