Add t-J model

.gitignore

@@ -1,2 +1,4 @@
 docs/build
 Manifest.toml
+.vscode/
+.DS_Store

src/MPSKitModels.jl

@@ -35,13 +35,15 @@ export c⁺, c⁻, c⁺⁺, c⁻⁻, c⁺⁻, c⁻⁺
 export e_plus, e_min, e_plusplus, e_minmin, e_plusmin, e_minplus
 export e_number, e_number_up, e_number_down, e_number_updown
 export e⁺⁺, e⁻⁻, e⁺⁻, e⁻⁺
+export TJOperators
 
 export transverse_field_ising
 export kitaev_model
 export quantum_potts
 export heisenberg_XXX, heisenberg_XXZ, heisenberg_XYZ
 export bilinear_biquadratic_model
 export hubbard_model, bose_hubbard_model
+export tj_model
 export quantum_chemistry_hamiltonian
 
 export classical_ising
@@ -65,6 +67,10 @@ include("operators/spinoperators.jl")
 include("operators/fermionoperators.jl")
 include("operators/hubbardoperators.jl")
 using .HubbardOperators
+# TJOperators share operator names with HubbardOperators
+# and is only imported to avoid name conflicts
+include("operators/tjoperators.jl")
+import .TJOperators
 include("operators/bosonoperators.jl")
 
 include("models/hamiltonians.jl")

src/models/hamiltonians.jl

@@ -370,3 +370,54 @@
 
     return H
 end
+
+#===========================================================================================
+    t-J models
+===========================================================================================#
+
+"""
+    tj_model([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}],
+                  [spin_symmetry::Type{<:Sector}], [lattice::AbstractLattice];
+                  t, J, mu, slave_fermion::Bool=false)
+
+MPO for the hamiltonian of the t-J model, as defined by
+```math
+H = -t \\sum_{\\langle i,j \\rangle, \\sigma}
+    (\\tilde{e}^\\dagger_{i,\\sigma} \\tilde{e}_{j,\\sigma} + h.c.)
+    + J \\sum_{\\langle i,j \\rangle}(\\mathbf{S}_i \\cdot \\mathbf{S}_j - \\frac{1}{4} n_i n_j)
+    - \\mu \\sum_i n_i
+```
+where ``\\tilde{e}_{i,\\sigma}`` is the electron operator with spin ``\\sigma`` restrict to the no-double-occupancy subspace. 
+"""
+function tj_model end
+function tj_model(lattice::AbstractLattice; kwargs...)
+    return tj_model(ComplexF64, Trivial, Trivial, lattice; kwargs...)
+end
+function tj_model(particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector};
+                  kwargs...)
+    return tj_model(ComplexF64, particle_symmetry, spin_symmetry; kwargs...)
+end
+function tj_model(elt::Type{<:Number}, lattice::AbstractLattice; kwargs...)
+    return tj_model(elt, Trivial, Trivial, lattice; kwargs...)
+end
+function tj_model(T::Type{<:Number}=ComplexF64,
+                  particle_symmetry::Type{<:Sector}=Trivial,
+                  spin_symmetry::Type{<:Sector}=Trivial,
+                  lattice::AbstractLattice=InfiniteChain(1);
+                  t=2.5, J=1.0, mu=0.0, slave_fermion::Bool=false)
+    hopping = TJOperators.e_plusmin(T, particle_symmetry, spin_symmetry; slave_fermion) +
+              TJOperators.e_minplus(T, particle_symmetry, spin_symmetry; slave_fermion)
+    num = TJOperators.e_number(T, particle_symmetry, spin_symmetry; slave_fermion)
+    heisenberg = TJOperators.S_exchange(T, particle_symmetry, spin_symmetry;
+                                        slave_fermion) -
+                 (1 / 4) * (num ⊗ num)
+    return @mpoham begin
+        sum(nearest_neighbours(lattice)) do (i, j)
+            return (-t) * hopping{i,j} + J * heisenberg{i,j}
+        end + sum(vertices(lattice)) do i
+            return (-mu) * num{i}
+        end
+    end
+end
+
+# TODO: add (hardcore) bosonic t-J model (https://arxiv.org/abs/2409.15424)

src/operators/hubbardoperators.jl

@@ -64,7 +64,7 @@ end
 """
     e_plusmin_up(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
 
-Return the two-body operator that creates a spin-up electron at the first site and annihilates a spin-up electron at the second.
+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.
 """
 e_plusmin_up(P::Type{<:Sector}, S::Type{<:Sector}) = e_plusmin_up(ComplexF64, P, S)
 function e_plusmin_up(T, ::Type{Trivial}, ::Type{Trivial})
@@ -111,7 +111,7 @@ const e⁺e⁻ꜛ = e_plusmin_up
 """
     e_plusmin_down(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
 
-Return the two-body operator that creates a spin-down electron at the first site and annihilates a spin-down electron at the second.
+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.
 """
 e_plusmin_down(P::Type{<:Sector}, S::Type{<:Sector}) = e_plusmin_down(ComplexF64, P, S)
 function e_plusmin_down(T, ::Type{Trivial}, ::Type{Trivial})
@@ -158,7 +158,9 @@ const e⁺e⁻ꜜ = e_plusmin_down
 """
     e_minplus_up(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
 
-Return the two-body operator that annihilates a spin-up electron at the first site and creates a spin-up electron at the second.
+Return the Hermitian conjugate of `e_plusmin_up`, 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.
 """
 e_minplus_up(P::Type{<:Sector}, S::Type{<:Sector}) = e_minplus_up(ComplexF64, P, S)
 function e_minplus_up(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
@@ -169,7 +171,9 @@ const e⁻⁺ꜛ = e_minplus_up
 """
     e_minplus_down(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})
 
-Return the two-body operator that annihilates a spin-down electron at the first site and creates a spin-down electron at the second.
+Return the Hermitian conjugate of `e_plusmin_down`, 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.
 """
 e_minplus_down(P::Type{<:Sector}, S::Type{<:Sector}) = e_minplus_down(ComplexF64, P, S)
 function e_minplus_down(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector})