Sudden switch of generalized Lieb-Robinson velocity in a transverse field Ising spin chain

TL;DR

This paper investigates the Lieb-Robinson velocity in a transverse field Ising spin chain, revealing a sudden speed switch related to the number of spins and demonstrating the velocity through various correlation measures.

Contribution

It demonstrates how to observe the Lieb-Robinson velocity in an Ising spin chain and uncovers a sudden switch in the velocity as the number of spins increases.

Findings

Lieb-Robinson velocity can be observed using multiple correlation measures.

A special behavior of correlation functions depends on spin parity.

The Lieb-Robinson speed exhibits a sudden switch with increasing spin number.

Abstract

The Lieb-Robinson theorem states that the speed at which the correlations between two distant nodes in a spin network can be built through local interactions has an upper bound, which is called the Lieb-Robinson velocity. Our central aim is to demonstrate how to observe the Lieb-Robinson velocity in an Ising spin chain with a strong transverse field. We adopt and compare four correlation measures for characterizing different types of correlations, which include correlation function, mutual information, quantum discord, and entanglement of formation. We prove that one of correlation functions shows a special behavior depending on the parity of the spin number. All the information-theoretical correlation measures demonstrate the existence of the Lieb-Robinson velocity. In particular, we find that there is a sudden switch of the Lieb-Robinson speed with the increasing of the number of spin.