diff --git a/Project.toml b/Project.toml
index 2861805..bf2ba2f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,7 @@ uuid = "abf2e61e-3022-5fcf-a868-69d409dee72b"
 version = "0.1.5"
 
 [deps]
+ClausenFunctions = "1cc96f36-ef02-40ef-a648-5e2c13df3076"
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -10,17 +11,16 @@ Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 QuantumOptics = "6e0679c1-51ea-5a7c-ac74-d61b76210b0c"
 QuantumOpticsBase = "4f57444f-1401-5e15-980d-4471b28d5678"
-Polylogarithms = "43cc4a2f-1a2b-4fbb-87e3-95c794af13de"
 
 [compat]
+ClausenFunctions = "1"
 Combinatorics = "1"
 DiffEqCallbacks = "2"
 Optim = "1"
 OrdinaryDiffEq = "6"
 QuantumOptics = "1"
-QuantumOpticsBase = "0.3"
-Polylogarithms = "0.1"
-julia = "1.4"
+QuantumOpticsBase = "0.4"
+julia = "1.6"
 
 [extras]
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
diff --git a/docs/Project.toml b/docs/Project.toml
index 7dd82fc..b2be7b8 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -4,6 +4,6 @@ PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee"
 QuantumOptics = "6e0679c1-51ea-5a7c-ac74-d61b76210b0c"
 
 [compat]
-Documenter = "~0.25"
+Documenter = "1"
 PyPlot = "2"
 QuantumOptics = "1"
diff --git a/docs/src/api.md b/docs/src/api.md
index 3cb59db..f9fad7d 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -54,6 +54,21 @@ geometry.box
 geometry.cube
 ```
 
+```@docs
+geometry.ring
+```
+
+```@docs
+geometry.lhc1
+```
+
+```@docs
+geometry.lhc1_p
+```
+
+```@docs
+geometry.excitation_phases
+```
 
 ## [Dipole-Dipole Interaction](@id API: Dipole-Dipole Interaction)
 
diff --git a/docs/src/geometry.md b/docs/src/geometry.md
index e0d28a3..2c66538 100644
--- a/docs/src/geometry.md
+++ b/docs/src/geometry.md
@@ -9,6 +9,7 @@ In order to simplify creation of various particle distributions, a few helper fu
 * [`geometry.hexagonal`](@ref)
 * [`geometry.box`](@ref)
 * [`geometry.cube`](@ref)
+* [`geometry.ring`](@ref)
 
 They can be used directly to create a [`SpinCollection`](@ref):
 
diff --git a/src/collective_modes.jl b/src/collective_modes.jl
index ddd3938..fc400cd 100644
--- a/src/collective_modes.jl
+++ b/src/collective_modes.jl
@@ -6,10 +6,9 @@ export Omega_k_chain, Gamma_k_chain, Omega_k_2D, Gamma_k_2D
 # atomic chains, see Asenjo-Garcia et al 10.1103/PhysRevX.7.031024.
 
 import LinearAlgebra
-import Polylogarithms
+using ClausenFunctions: cl2, cl3
 
 const la = LinearAlgebra
-const pl = Polylogarithms
 const k0 = 2pi
 const Rot90 = [0 -1; 1 0]
 
@@ -58,11 +57,9 @@ WLOG, this calculation scales natural atomic frequency wavelength lambda0=1 and
 """
 function Omega_k_chain(k::Real, a::Real, polarization::Array{<:Number, 1})  
     polarization, x_comp, yz_comp = polarization_renorm(polarization)
-    exp_sum = exp(im*(k0+k)*a)
-    exp_diff = exp(im*(k0-k)*a)
-    diag = pl.polylog(3, exp_sum) + pl.polylog(3, exp_diff) - im*k0*a*(pl.polylog(2, exp_sum) + pl.polylog(2, exp_diff))
-    perp = (k0*a)^2*(log(1-exp_sum) + log(1-exp_diff))
-    return 3/(4*(k0*a)^3) * (-2*x_comp*real(diag) + yz_comp*real(diag+perp))
+    diag = cl3((k0 + k)*a) + cl3((k0 - k)*a) + k0*a*(cl2((k0 + k)*a) + cl2((k0 - k)*a))
+    perp = (k0*a)^2*(log(1 - exp(im*(k0+k)*a)) + log(1 - exp(im*(k0-k)*a)))
+    return 3/(4*(k0*a)^3) * (-2*x_comp*diag + yz_comp*(diag+real(perp)))
 end