diff --git a/src/algorithms/toolbox.jl b/src/algorithms/toolbox.jl
index b995329f1..331d4ab36 100644
--- a/src/algorithms/toolbox.jl
+++ b/src/algorithms/toolbox.jl
@@ -6,10 +6,11 @@ Calculate the von Neumann entanglement entropy. The entropy can be computed from
 MPS state or directly from an entanglement spectrum as obtained from
 [`entanglement_spectrum`](@ref).
 
-When called on an MPS with an integer `site`, the entropy is computed across the
-entanglement cut to the right of site `site`. For `InfiniteMPS`, omitting `site` returns a
-vector of entropies, one for each site. For `FiniteMPS` and `WindowMPS`, `site` is
-required.
+When called on an MPS with an integer `site`, the entropy is computed for the bipartition that
+splits the chain between sites `site` and `site + 1`.
+`site = 0` therefore denotes the cut to the left of the first site.
+For `InfiniteMPS`, omitting `site` returns a vector of entropies, one for each site.
+For `FiniteMPS` and `WindowMPS`, `site` is required.
 """
 entropy(state::InfiniteMPS) = map(Base.Fix1(entropy, state), 1:length(state))
 function entropy(state::Union{FiniteMPS, WindowMPS, InfiniteMPS}, loc::Int)
@@ -80,21 +81,22 @@ end
 """
     entanglement_spectrum(ψ, site::Int) -> SectorVector{T, sectortype(ψ), AbstractVector{T}}
 
-Compute the entanglement spectrum at a given site, i.e. the singular values of the gauge
-matrix to the right of a given site. This is a vector containing the singular
-values. The contributions from specific sectors can be viewed by indexing accordingly, i.e.
+Compute the entanglement spectrum across the cut that splits the chain between sites `site` and
+`site + 1`, i.e. the singular values of the gauge tensor `ψ.C[site]`.
+The contributions from specific sectors can be viewed by indexing accordingly, i.e.
 `entanglement_spectrum(ψ, site)[sector]`.
 
-For `InfiniteMPS` and `WindowMPS` the default value for `site` is 0.
-
-For `FiniteMPS` no default value for `site` is given; it is up to the user to specify.
+`site` runs over `0:length(ψ)`.
+For `FiniteMPS`, `0` and `length(ψ)` are the cuts at the left and right edge of the chain.
+No default is given for `FiniteMPS`; it is up to the user to specify.
+For `WindowMPS` and `InfiniteMPS`, `site` defaults to `0`.
 """
 function entanglement_spectrum(st::Union{InfiniteMPS, WindowMPS}, site::Int = 0)
     checkbounds(st, site)
     return LinearAlgebra.svdvals(st.C[site])
 end
 function entanglement_spectrum(st::FiniteMPS, site::Int)
-    checkbounds(st, site)
+    checkbounds(st.C, site)
     return LinearAlgebra.svdvals(st.C[site])
 end
 
diff --git a/src/utility/plotting.jl b/src/utility/plotting.jl
index ec491693e..b58b912cc 100644
--- a/src/utility/plotting.jl
+++ b/src/utility/plotting.jl
@@ -32,8 +32,6 @@ function entanglementplot end
         sector_margin = 1 // 10, sector_formatter = string
     )
     mps = h.args[1]
-    (site <= length(mps) && !(isa(mps, FiniteMPS) && site == 0)) ||
-        throw(ArgumentError("Invalid site $site for the given mps."))
 
     spectra = entanglement_spectrum(mps, site)
     sectors = []
@@ -76,7 +74,7 @@ function entanglementplot end
     grid --> :xy
     widen --> true
 
-    xguide --> "χ = $(dim(left_virtualspace(mps, site)))"
+    xguide --> "χ = $(dim(_firstspace(mps.C[site])))"
     xticks --> (1:length(sectors), sector_formatter.(sectors))
     xtickfonthalign --> :center
     xtick_direction --> :out
diff --git a/test/states/finitemps.jl b/test/states/finitemps.jl
index 357e6793e..7e3796e02 100644
--- a/test/states/finitemps.jl
+++ b/test/states/finitemps.jl
@@ -146,6 +146,10 @@ end
         @test real(entropy(ψ, site)) >= 0
     end
 
+    @test entropy(ψ, 0) ≈ 0 atol = 1.0e-10 # trivial left bond
+    @test_throws BoundsError entanglement_spectrum(ψ, -1)
+    @test_throws BoundsError entanglement_spectrum(ψ, L + 1)
+
     # entropy is consistent with entanglement_spectrum
     for site in 1:L
         @test entropy(ψ, site) ≈ entropy(entanglement_spectrum(ψ, site))
@@ -155,7 +159,7 @@ end
     @test entropy(ψ, L) ≈ 0 atol = 1.0e-10
 
     # product state has zero entropy everywhere
-    ψ_product = FiniteMPS(rand, elt, L, d, oneunit(D))
+    ψ_product = FiniteMPS(rand, elt, L, d, unitspace(D))
     for site in 1:L
         @test entropy(ψ_product, site) ≈ 0 atol = 1.0e-10
     end