D-grading and quasifree evolution

TL;DR

This paper generalizes the connection between spin and Fermi systems on lattices, constructing an algebra for spin systems that admits quasifree evolutions, and analyzing the invariance and asymptotic properties of certain subalgebras.

Contribution

It introduces a new algebraic framework for spin systems with quasifree dynamics, extending previous relations between spin and Fermi systems.

Findings

Gauge invariant subalgebra remains invariant under quasifree evolution

Subalgebra is norm-asymptotically abelian under certain conditions

Framework applies to spin systems of arbitrary dimension d

Abstract

Generalizing the relation between spin-systems and Fermi-systems on the lattice we construct for a spin-system with dimension d an algebra for which quasifree time-evolutions exist. With appropriate assumptions the gauge invariant subalgebra common for both algebras is invariant under this time-evolution and on this subalgebra is norm-asymptotically abelian.