More corrections Holstein compared to PIMC and DMC

src/HolsteinTheory.jl

@@ -34,17 +34,17 @@ end
 """
 function holstein_interaction_energy_integrand(τ, v, w, α, ω, β; dims = 3)
 	coupling = holstein_coupling(1, α, ω; dims = dims)
-	propagator = polaron_propagator(τ, v, w, ω, β)
-	phonon_propagator(τ, ω, β) * (coupling * erf(π * sqrt(propagator * dims)) / sqrt(2π * propagator))^dims
+	propagator = polaron_propagator(τ, v, w, ω, β) * dims * 2 / ω
+	phonon_propagator(τ, ω, β) * (coupling * erf(π * sqrt(propagator / 2)) / sqrt(2π * propagator))^dims
 end
 
 """
 	Integrand for imaginary time integral for the holstein interaction energy at zero temperature. Here the k-space integral is evaluated analytically.
 """
 function holstein_interaction_energy_integrand(τ, v, w, α, ω; dims = 3)
 	coupling = holstein_coupling(1, α, ω; dims = dims)
-	propagator = polaron_propagator(τ, v, w, ω)
-	phonon_propagator(τ, ω) * (coupling * erf(π * sqrt(propagator * dims / ω)) / sqrt(2π * propagator))^dims
+	propagator = polaron_propagator(τ, v, w, ω) * 2 * dims / ω
+	phonon_propagator(τ, ω) * (coupling * erf(π * sqrt(propagator / 2)) / sqrt(2π * propagator))^dims
 end
 
 """
@@ -67,8 +67,8 @@ end
 	Total free energy for the Holstein model. Here the k-space integral is evaluated analytically.
 """
 function holstein_energy(v, w, α, ωβ...; dims = 3)
-	kinetic_energy = -2 * dims - electron_energy(v, w, ωβ...; dims = dims) / dims
-	potential_energy = -holstein_interaction_energy(v, w, α, ωβ...; dims = dims) / 2.0^dims
+	kinetic_energy = -2 * dims - electron_energy(v, w, ωβ...; dims = dims)
+	potential_energy = -holstein_interaction_energy(v, w, α, ωβ...; dims = dims) * dims
 	return (kinetic_energy + potential_energy), kinetic_energy, potential_energy
 end
 

src/KSpaceTheory.jl

@@ -34,7 +34,7 @@ end
 	Electron-phonon coupling matrix for the Holstein model.
 """
 function holstein_coupling(k, α, ω; dims = 3)
-	(2 * dims * α * ω)^(1/dims)
+	(dims * α * ω)^(1/dims)
 end
 
 """
@@ -117,14 +117,14 @@ end
 """
 function electron_energy(v, w, ω, β; dims = 3)
 	# dims / β / ω * (log(v / w) - 1 / 2 * log(2π * ω * β) - log(sinh(v * ω * β / 2) / sinh(w * ω * β / 2))) + dims / 4 * (v^2 - w^2) / v * (coth(v * ω * β / 2) - 2 / (v * ω * β)) * ω
-	(A(v, w, ω, β) + C(v, w, ω, β)) * dims / 3
+	(A(v, w, ω, β) + C(v, w, ω, β)) / 3
 end
 
 """
 	Energy associated with the free electron at zero temperature.
 """
 function electron_energy(v, w, ω; dims = 3)
-	-dims * (v - w) / 2 * ω + (dims / (4 * v)) * (v^2 - w^2) * ω
+	-(v - w) / 2 * ω + (1 / (4 * v)) * (v^2 - w^2) * ω
 end
 
 """