Boson operators

b_hopping([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b_hop([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

Return the two-body operator that describes a particle that hops between the first and the second site.

b_min([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁻([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic annihilation operator, with a maximum of cutoff bosons per site.

b_min_b_min([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁻b⁻([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic pair-annihilation operator, with a maximum of cutoff bosons per site.

b_min_b_plus([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁻b⁺([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic right-hopping operator, with a maximum of cutoff bosons per site.

b_num([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
n([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic number operator, with a maximum of cutoff bosons per site.

b_plus([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁺([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic creation operator, with a maximum of cutoff bosons per site.

b_plus_b_min([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁺b⁻([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic left-hopping operator, with a maximum of cutoff bosons per site.

b_plus_b_plus([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)
b⁺b⁺([elt::Type{<:Number}], [symmetry::Type{<:Sector}]; cutoff::Integer)

The truncated bosonic pair-creation operator, with a maximum of cutoff bosons per site.

basis_transform(symmetry::Type{<:Sector}; cutoff::Integer)

Return the unitary basis transformation that maps the occupation-number basis $\{|0⟩, |1⟩, …, |\mathrm{cutoff}⟩\}$ of boson_space(Trivial; cutoff) onto the basis of boson_space(symmetry; cutoff), as a TensorMap from boson_space(Trivial; cutoff) to desymmetrize(boson_space(symmetry; cutoff)), as required by symmetrize.

For U1Irrep, the boson number is used as the $U(1)$ charge, and the charge sectors are ordered as 0:cutoff. This coincides with the occupation-number basis, such that the transformation is the identity.

The transformations have exact integer entries and are therefore returned with integer scalar type, such that they promote to any scalar type without loss of precision.

boson_space([symmetry::Type{<:Sector}]; cutoff::Integer)

The local Hilbert space for a (truncated) bosonic system with a given symmetry and cutoff. Available symmetries are Trivial or U1Irrep.