Nonlocal pseudospin dynamics in a quantum Ising chain

Abstract

The existence of Majorana zero modes in nontrivial phase of quantum Ising chain results in not only the Kramers-like degeneracy spectrum, but also dynamic response for non-Hermitian perturbation in the ordered phase [\href{https://doi.org/10.1103/PhysRevLett.126.116401}{Phys. Rev. Lett. \textbf{126,} 116401 (2021)}]. In this work, we investigate the possible response of the degeneracy spectrum for Hermitian perturbations. We propose a single-particle description of the model in the ordered phase, associating with an internal degree of freedom characterized as a pseudospin. The effective magnetic field, arising from both local and nonlocal perturbations in terms of string operators, exerts on the pseudospin. We show that the action of string operator can be realized via a quench under the local perturbations. As an application, any ground states and excited states for the Hamiltonian with perturbation can be selected to identify the quantum phase, by adding the other perturbations to trigger a quench and measuring the Loschmidt echo.