Asymptotics for automorphisms of quantum systems on the lattice

TL;DR

This paper investigates the long-term behavior of automorphism groups in quantum lattice systems, revealing limitations on their asymptotic properties and implications for system symmetries.

Contribution

It demonstrates that continuous automorphism groups in quantum spin systems cannot become norm asymptotically abelian, unlike the shift automorphism, which cannot be extended continuously.

Findings

Shift automorphism is not norm asymptotically abelian.

Continuous automorphism groups lead to delocalization.

Shift cannot be extended continuously.

Abstract

We study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to delocalization but not to norm asymptotic abelianess. As a consequence the shift does not allow a continuous extension.