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