diff --git a/src/algorithms/approximate/idmrg.jl b/src/algorithms/approximate/idmrg.jl
index 0a80603b..7e18cac9 100644
--- a/src/algorithms/approximate/idmrg.jl
+++ b/src/algorithms/approximate/idmrg.jl
@@ -1,4 +1,4 @@
-function approximate(ost::MPSMultiline, toapprox::Tuple{<:MPOMultiline,<:MPSMultiline},
+function approximate(ost::MultilineMPS, toapprox::Tuple{<:MPOMultiline,<:MultilineMPS},
                      alg::IDMRG1, oenvs=environments(ost, toapprox))
     ψ = copy(ost)
     mpo, above = toapprox
@@ -52,12 +52,12 @@ function approximate(ost::MPSMultiline, toapprox::Tuple{<:MPOMultiline,<:MPSMult
         end
     end
 
-    nst = MPSMultiline(map(x -> x, ψ.AR); tol=alg.tol_gauge)
+    nst = MultilineMPS(map(x -> x, ψ.AR); tol=alg.tol_gauge)
     nenvs = environments(nst, toapprox)
     return nst, nenvs, ϵ
 end
 
-function approximate(ost::MPSMultiline, toapprox::Tuple{<:MPOMultiline,<:MPSMultiline},
+function approximate(ost::MultilineMPS, toapprox::Tuple{<:MPOMultiline,<:MultilineMPS},
                      alg::IDMRG2, oenvs=environments(ost, toapprox))
     length(ost) < 2 && throw(ArgumentError("unit cell should be >= 2"))
     mpo, above = toapprox
@@ -139,7 +139,7 @@ function approximate(ost::MPSMultiline, toapprox::Tuple{<:MPOMultiline,<:MPSMult
         end
     end
 
-    nst = MPSMultiline(map(x -> x, ψ.AR); tol=alg.tol_gauge)
+    nst = MultilineMPS(map(x -> x, ψ.AR); tol=alg.tol_gauge)
     nenvs = environments(nst, toapprox)
     return nst, nenvs, ϵ
 end
diff --git a/src/algorithms/changebonds/changebonds.jl b/src/algorithms/changebonds/changebonds.jl
index 0f06d21c..0c35bbc8 100644
--- a/src/algorithms/changebonds/changebonds.jl
+++ b/src/algorithms/changebonds/changebonds.jl
@@ -36,7 +36,7 @@ function _expand!(ψ::InfiniteMPS, AL′::PeriodicVector, AR′::PeriodicVector)
     end
     return normalize!(ψ)
 end
-function _expand!(ψ::MPSMultiline, AL′::PeriodicMatrix, AR′::PeriodicMatrix)
+function _expand!(ψ::MultilineMPS, AL′::PeriodicMatrix, AR′::PeriodicMatrix)
     for i in 1:size(ψ, 1)
         _expand!(ψ[i], AL′[i, :], AR′[i, :])
     end
diff --git a/src/algorithms/expval.jl b/src/algorithms/expval.jl
index 0f4caf52..ef97947f 100644
--- a/src/algorithms/expval.jl
+++ b/src/algorithms/expval.jl
@@ -118,9 +118,9 @@ function expectation_value(ψ::FiniteQP, mpo::FiniteMPO)
     return expectation_value(convert(FiniteMPS, ψ), mpo)
 end
 function expectation_value(ψ::InfiniteMPS, mpo::InfiniteMPO, envs...)
-    return expectation_value(convert(MPSMultiline, ψ), convert(MPOMultiline, mpo), envs...)
+    return expectation_value(convert(MultilineMPS, ψ), convert(MPOMultiline, mpo), envs...)
 end
-function expectation_value(ψ::MPSMultiline, O::MPOMultiline{<:Union{DenseMPO,SparseMPO}},
+function expectation_value(ψ::MultilineMPS, O::MPOMultiline{<:Union{DenseMPO,SparseMPO}},
                            envs::InfiniteMPOEnvironments=environments(ψ, O))
     return prod(product(1:size(ψ, 1), 1:size(ψ, 2))) do (i, j)
         GL = leftenv(envs, i, j, ψ)
@@ -130,7 +130,7 @@ function expectation_value(ψ::MPSMultiline, O::MPOMultiline{<:Union{DenseMPO,Sp
                  conj(ψ.AC[i + 1, j][1 4; 8])
     end
 end
-function expectation_value(ψ::MPSMultiline, mpo::MPOMultiline, envs...)
+function expectation_value(ψ::MultilineMPS, mpo::MPOMultiline, envs...)
     # TODO: fix environments
     return prod(x -> expectation_value(x...), zip(parent(ψ), parent(mpo)))
 end
diff --git a/src/algorithms/grassmann.jl b/src/algorithms/grassmann.jl
index 04b71497..9e6ab547 100644
--- a/src/algorithms/grassmann.jl
+++ b/src/algorithms/grassmann.jl
@@ -85,9 +85,9 @@ function ManifoldPoint(state::Union{InfiniteMPS,FiniteMPS}, envs)
     return ManifoldPoint(state, envs, g, Rhoreg)
 end
 
-function ManifoldPoint(state::MPSMultiline, envs)
+function ManifoldPoint(state::MultilineMPS, envs)
     # FIXME: add support for unitcells
-    @assert length(state.AL) == 1 "GradientGrassmann only supports MPSMultiline without unitcells for now"
+    @assert length(state.AL) == 1 "GradientGrassmann only supports MultilineMPS without unitcells for now"
 
     # TODO: this really should not use the operator from the environment
     f = expectation_value(state, envs.operator, envs)
@@ -128,8 +128,8 @@ function fg(x::ManifoldPoint{T}) where {T<:Union{InfiniteMPS,FiniteMPS}}
 
     return real(f), g_prec
 end
-function fg(x::ManifoldPoint{<:MPSMultiline})
-    @assert length(x.state) == 1 "GradientGrassmann only supports MPSMultiline without unitcells for now"
+function fg(x::ManifoldPoint{<:MultilineMPS})
+    @assert length(x.state) == 1 "GradientGrassmann only supports MultilineMPS without unitcells for now"
     # the gradient I want to return is the preconditioned gradient!
     g_prec = map(enumerate(x.g)) do (i, cg)
         return PrecGrad(rmul!(copy(cg), x.state.CR[i]'), x.Rhoreg[i])
@@ -145,9 +145,9 @@ function fg(x::ManifoldPoint{<:MPSMultiline})
 end
 
 """
-Retract a left-canonical MPSMultiline along Grassmann tangent `g` by distance `alpha`.
+Retract a left-canonical MultilineMPS along Grassmann tangent `g` by distance `alpha`.
 """
-function retract(x::ManifoldPoint{<:MPSMultiline}, tg, alpha)
+function retract(x::ManifoldPoint{<:MultilineMPS}, tg, alpha)
     g = reshape(tg, size(x.state))
 
     nal = similar(x.state.AL)
@@ -157,7 +157,7 @@ function retract(x::ManifoldPoint{<:MPSMultiline}, tg, alpha)
         h[i] = PrecGrad(th)
     end
 
-    nstate = MPSKit.MPSMultiline(nal, x.state.CR[:, end])
+    nstate = MPSKit.MultilineMPS(nal, x.state.CR[:, end])
     newpoint = ManifoldPoint(nstate, x.envs)
 
     return newpoint, h[:]