TJ operators

S_exchange(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the spin exchange operator S⋅S.

S_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the spin-minus operator.

S_minplus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator S⁻S⁺. The only nonzero matrix element corresponds to |↓↑⟩ <-- |↑↓⟩.

S_plus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the spin-plus operator.

S_plusmin(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator S⁺S⁻. The only nonzero matrix element corresponds to |↑↓⟩ <-- |↓↑⟩.

S_x(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body spin-1/2 x-operator on the electrons.

S_y(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body spin-1/2 x-operator on the electrons (only defined for Trivial symmetry).

S_z(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body spin-1/2 z-operator on the electrons.

c_min_c_plus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator that annihilates a particle at the first site and creates a particle at the second. This is the sum of u_min_u_plus and d_min_d_plus.

c_num(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body operator that counts the number of particles.

c_num_hole(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body operator that counts the number of holes.

c_plus_c_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator that creates a particle at the first site and annihilates a particle at the second. This is the sum of u_plus_u_min and d_plus_d_min.

c_singlet(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body singlet operator $(e_{1,↓} e_{2,↑} - e_{1,↓} e_{2,↑}) / sqrt(2)$.

d_min_d_plus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the Hermitian conjugate of d_plus_d_min, i.e. $(e†_{1,↓}, e_{2,↓})† = -e_{1,↓}, e†_{2,↓}$ (note the extra minus sign). It annihilates a spin-down electron at the first site and creates a spin-down electron at the second. The only nonzero matrix element corresponds to |0↓⟩ <-- |↓0⟩.

d_min_u_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator $e_{1,↓} e_{2,↑}$ that annihilates a spin-down particle at the first site and a spin-up particle at the second site. The only nonzero matrix element corresponds to |00⟩ <-- |↓↑⟩.

d_num(particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool=false)

Return the one-body operator that counts the number of spin-down electrons.

d_plus_d_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator $e†_{1,↓}, e_{2,↓}$ that creates a spin-down electron at the first site and annihilates a spin-down electron at the second. The only nonzero matrix element corresponds to |↓0⟩ <-- |0↓⟩.

tj_space(particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the local hilbert space for a t-J-type model with the given particle and spin symmetries. The possible symmetries are

• Particle number: Trivial, U1Irrep;
• Spin: Trivial, U1Irrep, SU2Irrep.

Setting slave_fermion = true switches to the slave-fermion basis.

• basis states for slave_fermion = false: |0⟩ = |vac⟩ (vacuum), |↑⟩ = (c↑)†|vac⟩, |↓⟩ = (c↓)†|vac⟩
• basis states for slave_fermion = true: (cσ = h† bσ; holon h is fermionic, spinon b_σ is bosonic): |0⟩ = h†|vac⟩, |↑⟩ = (b↑)†|vac⟩, |↓⟩ = (b↓)†|vac⟩

u_min_d_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator $e_{1,↑} e_{2,↓}$ that annihilates a spin-up particle at the first site and a spin-down particle at the second site. The only nonzero matrix element corresponds to |00⟩ <-- |↑↓⟩.

u_min_u_plus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the Hermitian conjugate of u_plus_u_min, i.e. $(e†_{1,↑}, e_{2,↑})† = -e_{1,↑}, e†_{2,↑}$ (note the extra minus sign). It annihilates a spin-up electron at the first site and creates a spin-up electron at the second. The only nonzero matrix element corresponds to |0↑⟩ <-- |↑0⟩.

u_num(particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the one-body operator that counts the number of spin-up electrons.

u_plus_u_min(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)

Return the two-body operator $e†_{1,↑}, e_{2,↑}$ that creates a spin-up electron at the first site and annihilates a spin-up electron at the second. The only nonzero matrix element corresponds to |↑0⟩ <-- |0↑⟩.