Improvement for Lieb-Robinson bounds and information transfer in spin chains

Takuro Matsuta, Tohru Koma, Shu Nakamura

Tomotaka Kuwahara

Mischa P. Woods

Kolja Them

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.

Vittorio Giovannetti, Rosario Fazio

Martin Gebert, Alvin Moon, Bruno Nachtergaele

We consider a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. We prove commutator bounds for its Heisenberg dynamics which incorporate the coupling strengths of the impurities. The impurities are assumed to satisfy a minimum spacing, and each impurity has a non-degenerate spectrum. Our results are proven in a broadly applicable setting, both in finite volume and in thermodynamic limit. We apply our results to improve Lieb–Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution.