A derivation of braided C*-tensor categories from gapped ground states satisfying the approximate Haag duality

  title={A derivation of braided C*-tensor categories from gapped ground states satisfying the approximate Haag duality},
  author={Yoshiko Ogata},
  journal={Journal of Mathematical Physics},
  • Y. Ogata
  • Published 29 June 2021
  • Physics, Mathematics
  • Journal of Mathematical Physics
We derive braided C∗-tensor categories from gapped ground states on two-dimensional quantum spin systems satisfying some additional condition which we call the approximate Haag duality. 
Classification of gapped ground state phases in quantum spin systems
Recently, classification problems of gapped ground state phases attract a lot of attention in quantum statistical mechanics. We explain about our operator algebraic approach to these problems.
A categorical Connes' $\chi(M)$
Popa introduced the tensor category χ̃(M) of approximately inner, centrally trivial bimodules of a II1 factor M , generalizing Connes’ χ(M). We extend Popa’s notions to define the W-tensor category
The split and approximate split property in 2D systems: stability and absence of superselection sectors
The split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if


Asymptotic Abelianness and Braided Tensor C*-Categories
By introducing the concepts of asymptopia and bi-asymptopia, we show how braided tensor C*-categories arise in a natural way. This generalizes constructions in algebraic quantum field theory by
Superselection sectors with braid group statistics and exchange algebras
The theory of superselection sectors is generalized to situations in which normal statistics has to be replaced by braid group statistics. The essential role of the positive Markov trace of algebraic
Haag duality for Kitaev's quantum double model for abelian groups
We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups.
Localized endomorphisms in Kitaev's toric code on the plane
We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground
An entropic invariant for 2D gapped quantum phases
We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based
The Complete Set of Infinite Volume Ground States for Kitaev’s Abelian Quantum Double Models
We study the set of infinite volume ground states of Kitaev’s quantum double model on $${\mathbb{Z}^2}$$Z2 for an arbitrary finite abelian group G. It is known that these models have a unique
On the Stability of Charges in Infinite Quantum Spin Systems
We consider a theory of superselection sectors for infinite quantum spin systems, describing charges that can be approximately localized in cone-like regions. The primary examples we have in mind are
Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms
Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of nonrelativistic quantum lattice systems is essentially bounded. We review works
An Introduction to the Classification of Amenable C-Algebras
The basics of C*-algebras amenable C*-algebras and K-theory AF-algebras and ranks of C*-algebras classification of simple AT-algebras C*-algebra extensions classification of simple amenable
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions