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Entanglement has developed into an essential concept for the characterizationof phases and phase transitions in ground states of quantum many-body systems.In this work, we use the logarithmic negativity to study the spatialentanglement structure in the transverse-field Ising chain both in the groundstate and at nonzero temperatures. Specifically, we investigate theentanglement between two disjoint blocks as a function of their separation,which can be viewed as the entanglement analog of a spatial correlationfunction. We find sharp entanglement thresholds at a critical distance beyondwhich the logarithmic negativity vanishes exactly and thus the two blocksbecome unentangled, which holds even in the presence of long-ranged quantumcorrelations, i.e., at the system's quantum critical point. Using Time-EvolvingBlock Decimation (TEBD), we explore this feature as a function of temperatureand size of the two blocks and present a simple model to describe our numericalobservations.

Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain