added J1-J2 model and transition calculation attempt, not really succ…

…essful

examples/J1J2Model.jl

@@ -0,0 +1,16 @@
+using fermions, Serialization
+include("../src/modelHamiltonians.jl")
+
+totalSites = 33
+@assert totalSites % 3 == 0
+partitions = collect(3:3:totalSites)
+J1byJ2Values = 0:0.1:2
+gapValues = zeros(length(J1byJ2Values))
+@time for (i, J1byJ2) in enumerate(J1byJ2Values)
+    hamiltonian = J1J2Model(J1byJ2, totalSites)
+    hamiltonianFlow = MinceHamiltonian(hamiltonian, partitions)
+    savePaths, results = IterDiag(hamiltonianFlow, 2000)
+    eigVals = deserialize(savePaths[end-1])["eigVals"]
+    gapValues[i] = eigVals[2] - eigVals[1]
+end
+display(gapValues)

src/modelHamiltonians.jl

@@ -379,3 +379,33 @@ function Dispersion(
     return dispersion
 end
 export Dispersion
+
+
+function J1J2Model(
+        J1byJ2::Float64,
+        numSites::Int64
+    )
+    J2 = 1.
+    J1 = J2 * J1byJ2
+    hamiltonian = Tuple{String, Vector{Int64}, Float64}[]
+    for site in 1:numSites-1
+        # J1 terms
+        push!(hamiltonian, ("nn", [site, site+1], J1))
+        push!(hamiltonian, ("n", [site], -J1/2))
+        push!(hamiltonian, ("n", [site+1], -J1/2))
+        push!(hamiltonian, ("+-", [site, site+1], J1/2))   
+        push!(hamiltonian, ("+-", [site+1, site], J1/2))   
+
+        if site == numSites-1
+            continue
+        end
+
+        # J2 terms
+        push!(hamiltonian, ("nn", [site, site+2], J2))
+        push!(hamiltonian, ("n", [site], -J2/2))
+        push!(hamiltonian, ("n", [site+2], -J2/2))
+        push!(hamiltonian, ("+-", [site, site+2], J2/2))   
+        push!(hamiltonian, ("+-", [site+2, site], J2/2))   
+    end
+    return hamiltonian
+end