English

On the structure of DHR bimodules of abstract spin chains

Quantum Algebra 2025-10-02 v2 Mathematical Physics math.MP Operator Algebras

Abstract

Abstract spin chains axiomatize the structure of local observables on the 1D lattice which are invariant under a global symmetry, and arise at the physical boundary of 2+1D topologically ordered spin systems. In this paper, we study tensor categorical properties of DHR bimodules over abstract spin chains. Assuming that the charge transporters generate the algebra of observables, we prove that the associated category has a structure of modular tensor category with respect to the natural braiding. Under an additional assumption of algebraic Haag duality, this category becomes the Drinfeld center of the half-line fusion category.

Keywords

Cite

@article{arxiv.2504.06094,
  title  = {On the structure of DHR bimodules of abstract spin chains},
  author = {Lucas Hataishi and David Jaklitsch and Corey Jones and Makoto Yamashita},
  journal= {arXiv preprint arXiv:2504.06094},
  year   = {2025}
}

Comments

v2: 30 pages, improved presentation and remarks on non-fusion case; v1: 29 pages