Effect of the Dzyaloshinskii-Moriya interaction on quantum speed limit and orthogonality catastrophe

We study the effect of the Dzyaloshinskii-Moriya (DM) interaction on the quantum speed limit (QSL) and orthogonality catastrophe (OC) in XY spin chains. With an initial sudden quench, the general expressions of fidelity and QSL time are derived in terms of the antisymmetric quasiparticle excitation spectra. The numerical and analytical studies show that depending on the system parameters, the DM interaction has various influences on QSL and fidelity. In general, the OC is witnessed and QSL time vanishes in the thermodynamic limit as the variance of the quenched Hamiltonian in ground states scales with the system size, and the conclusion is independent of the DM interaction strength. However, it is interesting to note that the QSL can uniquely detect the critical points and lines induced by the DM interaction. We further analyze the actual evolution speed, a measure of the criticality, and find its direct correspondence with the OC. We also study an interesting phenomenon arising from the magnetic field and DM interaction in the presence of classical noise. Notably, we find that the system dynamic is fault tolerant when the system is subject to a uniform classical noise in the DM interaction strength.