47 citations · 319 across the 21 of their papers we have counts for
21 papers
Local topological order, Haag duality, and reflection positivity
Pieter Naaijkens, David Penneys, Daniel Wallick
In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for abstract quantum spin systems which allow one to access topological order via a b…
Stacking and the triviality of invertible phases
Sven Bachmann, Alan Getz, Pieter Naaijkens +1
We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors o…
Holography for bulk-boundary local topological order
Corey Jones, Pieter Naaijkens, David Penneys
In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary (associated t…
The category of anyon sectors for non-abelian quantum double models
Alex Bols, Mahdie Hamdan, Pieter Naaijkens +1
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations…
Local topological order and boundary algebras
Corey Jones, Pieter Naaijkens, David Penneys +1
We introduce a set of axioms for locally topologically ordered quantum spin systems in terms of nets of local ground state projections, and we show they are satisfied by Kitaev's T…
The split and approximate split property in 2D systems: stability and absence of superselection sectors
Pieter Naaijkens, Yoshiko Ogata
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,…
An entropic invariant for 2D gapped quantum phases
Kohtaro Kato, Pieter Naaijkens
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 de…
On the stability of charges in infinite quantum spin systems
Matthew Cha, Pieter Naaijkens, Bruno Nachtergaele
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…
Subfactors and quantum information theory
Pieter Naaijkens
We consider quantum information tasks in an operator algebraic setting, where we consider normal states on von Neumann algebras. In particular, we consider subfactors $\mathfrak{N}…
The complete set of infinite volume ground states for Kitaev's abelian quantum double models
Matthew Cha, Pieter Naaijkens, Bruno Nachtergaele
We study the set of infinite volume ground states of Kitaev's quantum double model on for an arbitrary finite abelian group . It is known that these models have a…
Jones index, secret sharing and total quantum dimension
Leander Fiedler, Pieter Naaijkens, Tobias J. Osborne
We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we def…
Kitaev's quantum double model from a local quantum physics point of view
Pieter Naaijkens
A prominent example of a topologically ordered system is Kitaev's quantum double model for finite groups (which in particular includes , the…
On Enriching the Levin-Wen model with Symmetry
Liang Chang, Meng Cheng, Shawn X. Cui +6
Symmetry protected and symmetry enriched topological phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Lev…
Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems
Sven Bachmann, Wojciech Dybalski, Pieter Naaijkens
We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following t…
Haag duality for Kitaev's quantum double model for abelian groups
Leander Fiedler, Pieter Naaijkens
We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite…
Quantum spin systems on infinite lattices
Pieter Naaijkens
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an intr…
Kosaki-Longo index and classification of charges in 2D quantum spin models
Pieter Naaijkens
We consider charge superselection sectors of two-dimensional quantum spin models corresponding to cone localisable charges, and prove that the number of equivalence classes of such…
Haag duality and the distal split property for cones in the toric code
Pieter Naaijkens
We prove that Haag duality holds for cones in the toric code model. That is, for a cone Lambda, the algebra R_Lambda of observables localized in Lambda and the algebra R_{Lambda^c}…
Localized endomorphisms in Kitaev's toric code on the plane
Pieter Naaijkens
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 excit…
On the extension of stringlike localised sectors in 2+1 dimensions
Pieter Naaijkens
In the framework of algebraic quantum field theory, we study the category Δ_BF^A of stringlike localised representations of a net of observables O \mapsto A(O) in three dimensions.…
Four-point functions of different-weight operators in the AdS/CFT correspondence
León Berdichevsky, Pieter Naaijkens
We calculate four-point correlation functions of two weight-2 and two weight-3 1/2-BPS operators in \mathcal{N}=4 SYM in the large N limit in supergravity approximation. By the AdS…