Scaling of the local quantum uncertainty at quantum phase transitions

•LQU is suitable for the analysis of block correlations.•LQU exhibits pronounced behavior at quantum phase transitions.•LQU exponentially saturates in the quantum search.•Concavity of LQU indicates criticality in the Ising chain.

We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT.