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.