Hahn echo and criticality in spin-chain systems

TL;DR

This paper explores how Hahn spin-echo measurements can signal quantum phase transitions in spin-chain systems, revealing that critical points cause extremal echo values even at high temperatures.

Contribution

It establishes a novel relation between Hahn echo and quantum criticality in spin chains, with analytical results for the XY model at various temperatures.

Findings

Hahn echo exhibits extremal values at critical points

Criticality influences echo behavior at high temperatures

Relation explained between echo and phase transition

Abstract

We establish a relation between Hahn spin-echo of a spin-$\frac 1 2 $ particle and quantum phase transition in a spin-chain, which couples to the particle. The Hahn echo is calculated and discussed at zero as well as at finite temperatures. On the example of XY model, we show that the critical points of the chain are marked by the extremal values in the Hahn echo, and influence the Hahn echo in surprising high temperature. An explanation for the relation between the echo and criticality is also presented.