Scaling of the local quantum uncertainty at quantum phase transitions

TL;DR

This paper studies how local quantum uncertainty behaves at quantum phase transitions in different models, revealing scaling properties and critical behavior through analytical and numerical methods.

Contribution

It provides a detailed analysis of the scaling of local quantum uncertainty at both first- and second-order quantum phase transitions, combining analytical and numerical approaches.

Findings

LQU exhibits pronounced behavior at QPTs

Scaling laws of LQU near critical points

Analytical results for first-order QPTs and numerical for second-order

Abstract

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.