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Named Sectors: NamedSector

NamedSector represents the same Deligne tensor product as ProductSector, but stores its component sectors in a named tuple so that they can be accessed by name rather than by position. This is convenient when a product mixes several symmetries (e.g. a charge and a spin) and positional indexing would be error-prone.

Sector type

TensorKitSectors.NamedSector — Type
struct NamedSector{NT <: NamedSectorTuple}
NamedSector((; name₁=s₁, name₂=s₂, ...))

Represents the Deligne tensor product of sectors stored with named components. Similar to ProductSector, but components are accessible by name via s.name.

Examples

julia> s = NamedSector(; charge=U1Irrep(1), spin=SU2Irrep(1//2))
NamedSector(; charge=Irrep[U₁](1), spin=Irrep[SU₂](1/2))

julia> s.charge
Irrep[U₁](1)

julia> s.spin
Irrep[SU₂](1/2)
Warning

The sectors are stored internally in the s.sectors field, so the named components should not contain sectors as a name.

source
TensorKitSectors.@NamedSector — Macro
@NamedSector{name₁::T₁, name₂::T₂, ...}

Convenience macro for constructing a NamedSector type with named components, analogous to @NamedTuple.

Examples

julia> @NamedSector{charge::U1Irrep, spin::SU2Irrep}
NamedSector{@NamedTuple{charge::U1Irrep, spin::SU2Irrep}}

julia> (@NamedSector{charge::U1Irrep, spin::SU2Irrep})(U1Irrep(1), SU2Irrep(1//2))
NamedSector(; charge=Irrep[U₁](1), spin=Irrep[SU₂](1/2))
source

A named sector is constructed with keyword arguments to ⊠/NamedSector, or from a type built with the @NamedSector macro:

julia> s = ⊠(; charge = U1Irrep(1), spin = SU2Irrep(1//2))
NamedSector(; charge=Irrep[U₁](1), spin=Irrep[SU₂](1/2))

julia> s.charge
Irrep[U₁](1)

julia> s.spin
Irrep[SU₂](1/2)

julia> I = @NamedSector{charge::U1Irrep, spin::SU2Irrep}
NamedSector{@NamedTuple{charge::U1Irrep, spin::SU2Irrep}}

julia> I(U1Irrep(1), SU2Irrep(1//2))
NamedSector(; charge=Irrep[U₁](1), spin=Irrep[SU₂](1/2))

Fusion Rules

NamedSector behaves identically to the underlying ProductSector: fusion, duality, and units act componentwise, and every piece of topological data is forwarded to the corresponding ProductSector of the same components. Concretely, NamedSector converts to ProductSector (via ProductSector(s)) and delegates ⊗, Nsymbol, dual, unit, and allunits. See the ProductSector page for the componentwise fusion rules.

Topological Data

Fsymbol, Rsymbol, Asymbol, Bsymbol, fusiontensor, and dim are all computed by forwarding to the underlying ProductSector. Likewise, FusionStyle, BraidingStyle, UnitStyle, and the scalar-type traits are inherited from the product of the components.

Iteration

values(I) for a NamedSector type I iterates the same Cartesian product as the corresponding ProductSector, wrapping each result back into the named type. Indexing and findindex use the same ordering.

References