Direct calculation of the Lieb-Robinson correlation function for long Ising chains: Evidence of many-body localization

Direct calculation of the properties of multi-qubit/spin systems is often limited by the exponential scaling of the state space with system size. The recent development of the operator Pauli walk (OPW) method for 1D transverse-field Ising chains permits direct calculation of the Lieb-Robinson correlation function for hundreds or even thousands of qubits. This correlation function captures the non-commutativity of spatially and temporally separated local operators, thereby quantifying operator spreading and quantum information transport. The correlation front is seen to move down the chain with a velocity equal to that of the fastest free-fermion quasiparticle. We adapt the OPW method to the problem of disordered Ising chains. The results show the effect on information propagation of the Ising quantum phase transition. Vertical light cones provide clear evidence of many-body localization effects in these systems.