Superluminal moving defects in the Ising spin chain

TL;DR

This paper investigates how a defect moving faster than the maximum quasiparticle velocity in a quantum Ising chain influences local observables and the formation of a Local Quasi Stationary State, revealing unique superluminal effects.

Contribution

It introduces the concept of superluminal defects in the quantum Ising model and characterizes their impact on local observables and energy dissipation, providing exact results in specific impurity limits.

Findings

Superluminal defects induce a region of restored translational invariance.

The Local Quasi Stationary State (LQSS) is strongly affected by defect velocity.

Friction force reflects energy cost of LQSS formation.

Abstract

Quantum excitations in lattice systems always propagate at a finite maximum velocity. We probe this mechanism by considering a defect travelling at a constant velocity in the quantum Ising spin chain in transverse field. Independently of the microscopic details of the defect, we characterize the expectation value of local observables at large times and large distances from the impurity, where a Local Quasi Stationary State (LQSS) emerges. The LQSS is strongly affected by the defect velocity: for superluminal defects, it exhibits a growing region where translational invariance is spontaneously restored. We also analyze the behavior of the friction force exerted by the many-body system on the moving defect, which reflects the energy required by the LQSS formation. Exact results are provided in the two limits of extremely narrow and very smooth impurity. Possible extensions to more general free-fermion models and interacting systems are discussed