Add sigma t-J model

Author: Yue-Zhengyuan

src/models/hamiltonians.jl

@@ -383,16 +383,25 @@ end
 """
     tj_model([elt::Type{<:Number}], [particle_symmetry::Type{<:Sector}],
                   [spin_symmetry::Type{<:Sector}], [lattice::AbstractLattice];
-                  t, J, mu, slave_fermion::Bool=false)
+                  t, J, mu, slave_fermion::Bool=false, sigma::Bool=false)
 
-MPO for the hamiltonian of the t-J model, as defined by
+MPO for the hamiltonian of the t-J model or the sigma t-J model, 
 ```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)
+H = H_t + 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. 
+where the hopping term is
+```math
+H_t = -t \\sum_{\\langle i,j \\rangle, \\sigma}
+    (\\tilde{e}^\\dagger_{i,\\sigma} \\tilde{e}_{j,\\sigma} + h.c.)
+```
+for the t-J model (with `sigma = false`), or 
+```math
+H = -t \\sum_{\\langle i,j \\rangle, \\sigma} \\sigma
+    (\\tilde{e}^\\dagger_{i,\\sigma} \\tilde{e}_{j,\\sigma} + h.c.)
+```
+for the sigma t-J model (with `sigma = true`, introduced in https://doi.org/10.1038/srep02586).
+In both cases, ``\\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...)
@@ -409,9 +418,11 @@ 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)
+                  t=2.5, J=1.0, mu=0.0, slave_fermion::Bool=false, sigma::Bool=false)
+    hopping = TJOperators.e_plusmin(T, particle_symmetry, spin_symmetry; slave_fermion,
+                                    sigma) +
+              TJOperators.e_minplus(T, particle_symmetry, spin_symmetry; slave_fermion,
+                                    sigma)
     num = TJOperators.e_number(T, particle_symmetry, spin_symmetry; slave_fermion)
     heisenberg = TJOperators.S_exchange(T, particle_symmetry, spin_symmetry;
                                         slave_fermion) -

src/operators/tjoperators.jl

@@ -212,33 +212,43 @@ end
 const e⁻e⁺ꜜ = e_minplus_down
 
 """
-    e_plusmin(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)
+    e_plusmin(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false, sigma::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 `e_plusmin_up` and `e_plusmin_down`.
+This is defined as `e_plusmin_up + e_plusmin_down` when `sigma = false`, 
+or `e_plusmin_up - e_plusmin_down` when `sigma = true`.
 """
-function e_plusmin(P::Type{<:Sector}, S::Type{<:Sector}; slave_fermion::Bool=false)
-    return e_plusmin(ComplexF64, P, S; slave_fermion)
+function e_plusmin(P::Type{<:Sector}, S::Type{<:Sector}; slave_fermion::Bool=false,
+                   sigma::Bool=false)
+    return e_plusmin(ComplexF64, P, S; slave_fermion, sigma)
 end
 function e_plusmin(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector};
-                   slave_fermion::Bool=false)
-    return e_plusmin_up(T, particle_symmetry, spin_symmetry; slave_fermion) +
-           e_plusmin_down(T, particle_symmetry, spin_symmetry; slave_fermion)
+                   slave_fermion::Bool=false, sigma::Bool=false)
+    return if sigma
+        e_plusmin_up(T, particle_symmetry, spin_symmetry; slave_fermion) -
+        e_plusmin_down(T, particle_symmetry, spin_symmetry; slave_fermion)
+    else
+        e_plusmin_up(T, particle_symmetry, spin_symmetry; slave_fermion) +
+        e_plusmin_down(T, particle_symmetry, spin_symmetry; slave_fermion)
+    end
 end
 const e⁺e⁻ = e_plusmin
 
 """
-    e_minplus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false)
+    e_minplus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector}; slave_fermion::Bool = false, sigma::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 `e_minplus_up` and `e_minplus_down`.
+This is defined as `e_minplus_up + e_minplus_down` when `sigma = false`, 
+or `e_minplus_up - e_minplus_down` when `sigma = true`.
 """
-function e_minplus(P::Type{<:Sector}, S::Type{<:Sector}; slave_fermion::Bool=false)
-    return e_minplus(ComplexF64, P, S; slave_fermion)
+function e_minplus(P::Type{<:Sector}, S::Type{<:Sector}; slave_fermion::Bool=false,
+                   sigma::Bool=false)
+    return e_minplus(ComplexF64, P, S; slave_fermion, sigma)
 end
 function e_minplus(T, particle_symmetry::Type{<:Sector}, spin_symmetry::Type{<:Sector};
-                   slave_fermion::Bool=false)
-    return copy(adjoint(e_plusmin(T, particle_symmetry, spin_symmetry; slave_fermion)))
+                   slave_fermion::Bool=false, sigma::Bool=false)
+    return copy(adjoint(e_plusmin(T, particle_symmetry, spin_symmetry; slave_fermion,
+                                  sigma)))
 end
 const e⁻e⁺ = e_minplus
 

test/tjoperators.jl

@@ -9,6 +9,7 @@ implemented_symmetries = [(Trivial, Trivial),
                           (U1Irrep, U1Irrep)]
 @testset "basic properties" begin
     for slave_fermion in (false, true),
+        sigma in (false, true),
         particle_symmetry in (Trivial, U1Irrep),
         spin_symmetry in (Trivial, U1Irrep, SU2Irrep)