Towards experimental tests and applications of Lieb-Robinson bounds

TL;DR

This paper explores the experimental verification of Lieb-Robinson bounds using spin-polarized scanning tunneling microscopy, revealing discrepancies and potential for improving bounds, with implications for spintronic device signal speeds.

Contribution

It simplifies the most general Lieb-Robinson bound and demonstrates its application as an upper limit for signal speed in spintronic devices, highlighting discrepancies with actual velocities.

Findings

Discrepancy of approximately 4 between bound limit and actual velocities.

Simplification of the most general Lieb-Robinson bound.

Potential to modify real signal propagation independently of bounds.

Abstract

Spin-polarized scanning tunneling microscopy is identified as a suitable experimental technique to investigate the quantitative quality of Lieb-Robinson bounds on the signal velocity. The latest, most general bound is simplified and it is shown that there is a discrepancy by a factor of approximately 4 between the corresponding limit speed and some estimated exact velocities in atomic spin chains. The observed discrepancy facilitates conclusions for a further mathematical improvement of Lieb-Robinson bounds. The real signal propagation can be modified with several experimental parameters from which the bounds are independent. This enables the application of Lieb-Robinson bounds as upper limits on the enhancement of the real signal speed for information transport in spintronic devices.