Ground states of the infinite q-deformed Heisenberg ferromagnet

摘要: We set up a general structure for the analysis of ``frustration-free ground states'', or ``zero-energy i.e., states minimizing each term in lattice interaction individually. The nesting finite volume state spaces is described by generalized inductive limit observable algebras. space this system has which canonically isomorphic (as compact convex set) to zero-energy states. show that Heisenberg ferromagnets, and valence bond solid states, an abelian C*-algebra, all are translationally invariant periodic. For $q$-deformed spin-$1/2$ ferromagnet one dimension (i.e., XXZ-chain with S$_q$U(2)-invariant boundary conditions) extension non-commutative algebra operators two points, corresponding ``all spins up'' down'' respectively. These only remaining ones parametrized density matrices on Hilbert space, converge weakly (resp.\ down'') shifts $-\infty$ $+\infty$).