Hubbard operators
TensorKitTensors.HubbardOperators.S_exchange — FunctionS_exchange(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the spin exchange operator S⋅S.
TensorKitTensors.HubbardOperators.S_min — FunctionS_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
S⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the spin-minus operator (only defined for Trivial spin symmetry).
TensorKitTensors.HubbardOperators.S_min_S_plus — FunctionS_min_S_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
S⁻S⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator S⁻S⁺. The only nonzero matrix element corresponds to |↓,↑⟩ <-- |↑,↓⟩.
TensorKitTensors.HubbardOperators.S_plus — FunctionS_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
S⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the spin-plus operator S⁺ = e†_↑ e_↓ (only defined for Trivial spin symmetry).
TensorKitTensors.HubbardOperators.S_plus_S_min — FunctionS_plus_S_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
S⁺S⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator S⁺S⁻. The only nonzero matrix element corresponds to |↑,↓⟩ <-- |↓,↑⟩.
TensorKitTensors.HubbardOperators.S_x — FunctionS_x(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
Sˣ(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the one-body spin-1/2 x-operator on the electrons (only defined for Trivial symmetry). .
TensorKitTensors.HubbardOperators.S_y — FunctionS_y(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
Sʸ(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the one-body spin-1/2 y-operator on the electrons (only defined for Trivial symmetry).
TensorKitTensors.HubbardOperators.S_z — FunctionS_z(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
Sᶻ(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the one-body spin-1/2 z-operator on the electrons.
TensorKitTensors.HubbardOperators.d_min_d_min — Functiond_min_d_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
d⁻d⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator $e_{1,↓} e_{2,↓}$ that annihilates a spin-down particle at both sites. The nonzero matrix elements are
-|0,0⟩ ↤ |↓,↓⟩, +|0,↑⟩ ↤ |↓,↑↓⟩
-|↑,0⟩ ↤ |↑↓,↓⟩, +|↑,↑⟩ ↤ |↑↓,↑↓⟩TensorKitTensors.HubbardOperators.d_min_d_plus — Functiond_min_d_plus([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
d⁻d⁺([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the two-body operator $e_{1,↓}, e†_{2,↓}$ that annihilates a spin-down particle at the first site and creates a spin-down particle at the second.
TensorKitTensors.HubbardOperators.d_min_u_min — Functiond_min_u_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
d⁻u⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})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 nonzero matrix elements are
-|0,0⟩ ↤ |↓,↑⟩, -|0,↓⟩ ↤ |↓,↑↓⟩
-|↑,0⟩ ↤ |↑↓,↑⟩, -|↑,↓⟩ ↤ |↑↓,↑↓⟩TensorKitTensors.HubbardOperators.d_num — Functiond_num([particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
nꜜ([particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the one-body operator that counts the number of spin-down particles.
TensorKitTensors.HubbardOperators.d_plus_d_min — Functiond_plus_d_min([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
d⁺d⁻([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the two-body operator $e†_{1,↓}, e_{2,↓}$ that creates a spin-down particle at the first site and annihilates a spin-down particle at the second.
TensorKitTensors.HubbardOperators.d_plus_d_plus — Functiond_plus_d_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
d⁺d⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator $e†_{1,↓} e†_{2,↓}$ that creates a spin-down particle at both sites. The nonzero matrix elements are
TensorKitTensors.HubbardOperators.d_plus_u_plus — Functiond_plus_u_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
d⁺u⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator $e†_{1,↓} e†_{2,↑}$ that creates a spin-down particle at the first site and a spin-up particle at the second site.
TensorKitTensors.HubbardOperators.e_hop — Functione_hopping([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
e_hop([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the two-body operator that describes a particle that hops between the first and the second site.
TensorKitTensors.HubbardOperators.e_min_e_plus — Functione_min_e_plus([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
e⁻e⁺([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])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.
TensorKitTensors.HubbardOperators.e_num — Functione_num([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
n([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the one-body operator that counts the number of particles.
TensorKitTensors.HubbardOperators.e_plus_e_min — Functione_plus_e_min([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
e⁺e⁻([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])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.
TensorKitTensors.HubbardOperators.hubbard_space — Functionhubbard_space(particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the local hilbert space for a Hubbard-type model with the given particle and spin symmetries. The four basis states are
|0⟩ (vacuum), |↑⟩ = (c↑)†|0⟩, |↓⟩ = (c↓)†|0⟩, |↑↓⟩ = (c↑)†(c↓)†|0⟩.The possible symmetries are Trivial, U1Irrep, and SU2Irrep, for both particle number and spin.
TensorKitTensors.HubbardOperators.singlet_min — Functionsinglet_min(elt, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
singlet⁻(elt, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the adjoint of singlet_plus operator, which is $(-e_{1,↑} e_{2,↓} + e_{1,↓} e_{2,↑}) / sqrt(2)$
TensorKitTensors.HubbardOperators.singlet_plus — Functionsinglet_plus(elt, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
singlet⁺(elt, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body singlet operator $(e^†_{1,↑} e^†_{2,↓} - e^†_{1,↓} e^†_{2,↑}) / sqrt(2)$, which creates the singlet state when acting on vaccum.
TensorKitTensors.HubbardOperators.u_min_d_min — Functionu_min_d_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
u⁻d⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})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 nonzero matrix elements are
-|0,0⟩ ↤ |↑,↓⟩, +|0,↑⟩ ↤ |↑,↑↓⟩,
+|↓,0⟩ ↤ |↑↓,↓⟩, -|↓,↑⟩ ↤ |↑↓,↑↓⟩TensorKitTensors.HubbardOperators.u_min_u_min — Functionu_min_u_min(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
u⁻u⁻(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator $e_{1,↑} e_{2,↑}$ that annihilates a spin-up particle at both sites. The nonzero matrix elements are
-|0,0⟩ ↤ |↑,↑⟩, -|0,↓⟩ ↤ |↑,↑↓⟩
+|↓,0⟩ ↤ |↑↓,↑⟩, +|↓,↓⟩ ↤ |↑↓,↑↓⟩TensorKitTensors.HubbardOperators.u_min_u_plus — Functionu_min_u_plus([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
u⁻u⁺([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the two-body operator $e_{1,↑}, e†_{2,↑}$ that annihilates a spin-up particle at the first site and creates a spin-up particle at the second.
TensorKitTensors.HubbardOperators.u_num — Functionu_num([particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
nꜛ([particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the one-body operator that counts the number of spin-up particles.
TensorKitTensors.HubbardOperators.u_plus_d_plus — Functionu_plus_d_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
u⁺d⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})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.
TensorKitTensors.HubbardOperators.u_plus_u_min — Functionu_plus_u_min([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
u⁺u⁻([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the two-body operator $e†_{1,↑}, e_{2,↑}$ that creates a spin-up particle at the first site and annihilates a spin-up particle at the second.
TensorKitTensors.HubbardOperators.u_plus_u_plus — Functionu_plus_u_plus(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
u⁺u⁺(elt::Type{<:Number}, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})Return the two-body operator $e†_{1,↑} e†_{2,↑}$ that creates a spin-up particle at both sites.
TensorKitTensors.HubbardOperators.ud_num — Functionud_num([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])
nꜛꜜ([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}], [spin_symmetry::Type{<:Sector}])Return the one-body operator that counts the number of doubly occupied sites.