Strict deformation quantization and local spin interactions

Abstract

We define a strict deformation quantization which is compatible with any Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a spin chain. This is a generalization of previous results known for mean-field theories. The main idea is to study the asymptotic properties of a suitably defined algebra of sequences invariant under the group generated by a cyclic permutation. Our point of view is similar to the one adopted by Landsman, Moretti and van de Ven, who considered a strict deformation quantization for the case of mean-field theories. However, the methods for a local spin interaction are considerably more involved, due to the presence of a strictly smaller symmetry group.

arXiv comment39 pages

References in corpus (6)

• Strict deformation quantization of the state space of $M_k(\mathbb{C})$ with applications to the Curie-Weiss model
• The classical limit and spontaneous symmetry breaking in algebraic quantum theory
• Bulk-boundary asymptotic equivalence of two strict deformation quantizations
• The classical limit of mean-field quantum spin systems
• DLR-KMS correspondence on lattice spin systems
• Injective tensor products in strict deformation quantization

Cited by in corpus (1)

• Classical and quantum KMS states on spin lattice systems