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 …
corresponding to the translational invariant ground state of Kitaev's quantum double model …
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 …
charges that can be approximately localized in cone-like regions. The primary examples we …
On Landauer's principle and bound for infinite systems
R Longo - Communications in Mathematical Physics, 2018 - Springer
Landauer's principle provides a link between Shannon's information entropy and Clausius'
thermodynamical entropy. Here we set up a basic formula for the incremental free energy of …
thermodynamical entropy. Here we set up a basic formula for the incremental free energy of …
Boundary states of a bulk gapped ground state in 2-d quantum spin systems
Y Ogata - Communications in Mathematical Physics, 2024 - Springer
We introduce a natural mathematical definition of boundary states of a bulk gapped ground
state in the operator algebraic framework of 2-D quantum spin systems. With the …
state in the operator algebraic framework of 2-D quantum spin systems. With the …
An operator algebraic approach to symmetry defects and fractionalization
We provide a superselection theory of symmetry defects in 2+ 1D symmetry enriched
topological (SET) order in the infinite volume setting. For a finite symmetry group $ G $ with a …
topological (SET) order in the infinite volume setting. For a finite symmetry group $ G $ with a …
On gapped phases with a continuous symmetry and boundary operators
We discuss the role of compact symmetry groups, G, in the classification of gapped ground
state phases of quantum spin systems. We consider two representations of G on infinite …
state phases of quantum spin systems. We consider two representations of G on infinite …
Superselection sectors for posets of von Neumann algebras
A Bhardwaj, T Brisky, CY Chuah, K Kawagoe… - arxiv preprint arxiv …, 2024 - arxiv.org
We study a commutant-closed collection of von Neumann algebras acting on a common
Hilbert space indexed by a poset with an order-reversing involution. We give simple …
Hilbert space indexed by a poset with an order-reversing involution. We give simple …
The split and approximate split property in 2D systems: stability and absence of superselection sectors
P Naaijkens, Y Ogata - Communications in Mathematical Physics, 2022 - Springer
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 …
understood as the entanglement between the two subsystems being weak. From this point of …
An algebraic quantum field theoretic approach to toric code with gapped boundary
D Wallick - Journal of Mathematical Physics, 2023 - pubs.aip.org
Topologically ordered quantum spin systems have become an area of great interest, as they
may provide a fault-tolerant means of quantum computation. One of the simplest examples …
may provide a fault-tolerant means of quantum computation. One of the simplest examples …
Kitaev's quantum double model from a local quantum physics point of view
P Naaijkens - Advances in algebraic quantum field theory, 2015 - Springer
A prominent example of a topologically ordered system is Kitaev's quantum double model D
(G) for finite groups G (which in particular includes G= Z _2, the toric code). We will look at …
(G) for finite groups G (which in particular includes G= Z _2, the toric code). We will look at …