diff --git a/Project.toml b/Project.toml
index 46218a1..4653691 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "GradedArrays"
 uuid = "bc96ca6e-b7c8-4bb6-888e-c93f838762c2"
-version = "0.7.0"
+version = "0.7.1"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 
 [workspace]
@@ -43,12 +43,12 @@ HalfIntegers = "1.6"
 KroneckerArrays = "0.3.27"
 LinearAlgebra = "1.10"
 MatrixAlgebraKit = "0.6"
-NamedDimsArrays = "0.13, 0.14"
+NamedDimsArrays = "0.15"
 Random = "1.10"
 SUNRepresentations = "0.3"
 SparseArraysBase = "0.9"
 SplitApplyCombine = "1.2.3"
-TensorAlgebra = "0.7.20"
+TensorAlgebra = "0.8"
 TensorKitSectors = "0.3"
 TypeParameterAccessors = "0.4"
 julia = "1.10"
diff --git a/src/broadcast.jl b/src/broadcast.jl
index fd9cec5..c11554f 100644
--- a/src/broadcast.jl
+++ b/src/broadcast.jl
@@ -1,6 +1,5 @@
 using Base.Broadcast: Broadcast as BC
-using FillArrays: Zeros, fillsimilar
-using TensorAlgebra: TensorAlgebra, *ₗ, +ₗ, -ₗ, /ₗ, conjed
+using TensorAlgebra: TensorAlgebra
 
 struct SectorStyle{I, N} <: BC.AbstractArrayStyle{N} end
 SectorStyle{I, N}(::Val{M}) where {I, N, M} = SectorStyle{I, M}()
@@ -31,21 +30,17 @@ function Base.Broadcast.materialize(a::SectorArray)
     return ofsector(a, Base.Broadcast.materialize(a.data))
 end
 
-function TensorAlgebra.:+ₗ(a::SectorArray, b::SectorArray)
-    _check_add_axes(a, b)
-    return ofsector(a, a.data +ₗ b.data)
-end
-
-function TensorAlgebra.:*ₗ(α::Number, a::SectorArray)
-    return ofsector(a, α *ₗ a.data)
-end
-TensorAlgebra.:*ₗ(a::SectorArray, α::Number) = α *ₗ a
-function TensorAlgebra.conjed(a::SectorArray)
-    return ofsector(a, TensorAlgebra.conjed(a.data))
+function Base.similar(bc::BC.Broadcasted{<:SectorStyle}, elt::Type, ax)
+    bc′ = BC.flatten(bc)
+    arg = bc′.args[findfirst(arg -> arg isa SectorArray, bc′.args)]
+    return ofsector(arg, similar(arg.data, elt))
 end
 
-function BC.broadcasted(style::SectorStyle, f, args...)
-    return TensorAlgebra.broadcasted_linear(style, f, args...)
+function Base.copyto!(dest::SectorArray, bc::BC.Broadcasted{<:SectorStyle})
+    lb = TensorAlgebra.tryflattenlinear(bc)
+    isnothing(lb) &&
+        throw(ArgumentError("SectorArray broadcasting requires linear operations"))
+    return copyto!(dest, lb)
 end
 
 struct GradedStyle{I, N, B <: BC.AbstractArrayStyle{N}} <: BC.AbstractArrayStyle{N}
@@ -90,67 +85,6 @@ function Base.similar(bc::BC.Broadcasted{<:GradedStyle}, elt::Type, ax)
     return graded_similar(arg, elt, ax)
 end
 
-function _check_add_axes(a::AbstractArray, b::AbstractArray)
-    axes(a) == axes(b) ||
-        throw(
-        ArgumentError("linear broadcasting requires matching axes")
-    )
-    return nothing
-end
-
-function lazyblock(a::GradedArray{<:Any, N}, I::Vararg{Block{1}, N}) where {N}
-    if isstored(a, I...)
-        return blocks(a)[Int.(I)...]
-    else
-        block_ax = map((ax, i) -> eachblockaxis(ax)[Int(i)], axes(a), I)
-        return fillsimilar(Zeros{eltype(a)}(block_ax), block_ax)
-    end
-end
-lazyblock(a::GradedArray, I::Block) = lazyblock(a, Tuple(I)...)
-
-TensorAlgebra.@scaledarray_type ScaledGradedArray
-TensorAlgebra.@scaledarray ScaledGradedArray
-TensorAlgebra.@conjarray_type ConjGradedArray
-TensorAlgebra.@conjarray ConjGradedArray
-TensorAlgebra.@addarray_type AddGradedArray
-TensorAlgebra.@addarray AddGradedArray
-
-const LazyGradedArray = Union{
-    GradedArray, ScaledGradedArray, ConjGradedArray, AddGradedArray,
-}
-
-function TensorAlgebra.BroadcastStyle_scaled(arrayt::Type{<:ScaledGradedArray})
-    return BC.BroadcastStyle(TensorAlgebra.unscaled_type(arrayt))
-end
-function TensorAlgebra.BroadcastStyle_conj(arrayt::Type{<:ConjGradedArray})
-    return BC.BroadcastStyle(TensorAlgebra.conjed_type(arrayt))
-end
-function TensorAlgebra.BroadcastStyle_add(arrayt::Type{<:AddGradedArray})
-    args_type = TensorAlgebra.addends_type(arrayt)
-    return Base.promote_op(BC.combine_styles, fieldtypes(args_type)...)()
-end
-
-function lazyblock(a::ScaledGradedArray, I::Block)
-    return TensorAlgebra.coeff(a) *ₗ lazyblock(TensorAlgebra.unscaled(a), I)
-end
-function lazyblock(a::ConjGradedArray, I::Block)
-    return conjed(lazyblock(conjed(a), I))
-end
-function lazyblock(a::AddGradedArray, I::Block)
-    return +ₗ(map(Base.Fix2(lazyblock, I), TensorAlgebra.addends(a))...)
-end
-
-# TODO: Use `eachblockstoredindex` directly for lazy graded wrappers and delete the
-# `graded_eachblockstoredindex` helper once that refactor is split into its own PR.
-graded_eachblockstoredindex(a::GradedArray) = collect(eachblockstoredindex(a))
-function graded_eachblockstoredindex(a::ScaledGradedArray)
-    return graded_eachblockstoredindex(TensorAlgebra.unscaled(a))
-end
-graded_eachblockstoredindex(a::ConjGradedArray) = graded_eachblockstoredindex(conjed(a))
-function graded_eachblockstoredindex(a::AddGradedArray)
-    return unique!(vcat(map(graded_eachblockstoredindex, TensorAlgebra.addends(a))...))
-end
-
 # TODO: Rename `graded_similar` to `similar_graded` or fold it into `similar`
 # entirely once the follow-up allocator cleanup is ready.
 function graded_similar(
@@ -160,52 +94,10 @@ function graded_similar(
     ) where {N}
     return similar(a, elt, ax)
 end
-function graded_similar(
-        a::ScaledGradedArray,
-        elt::Type,
-        ax::NTuple{N, <:GradedUnitRange}
-    ) where {N}
-    return graded_similar(TensorAlgebra.unscaled(a), elt, ax)
-end
-function graded_similar(
-        a::ConjGradedArray,
-        elt::Type,
-        ax::NTuple{N, <:GradedUnitRange}
-    ) where {N}
-    return graded_similar(conjed(a), elt, ax)
-end
-function graded_similar(
-        a::AddGradedArray,
-        elt::Type,
-        ax::NTuple{N, <:GradedUnitRange}
-    ) where {N}
-    style = BC.combine_styles(TensorAlgebra.addends(a)...)
-    bc = BC.Broadcasted(style, +, TensorAlgebra.addends(a))
-    return similar(bc, elt, ax)
-end
-
-function copy_lazygraded(a::LazyGradedArray)
-    c = graded_similar(a, eltype(a), axes(a))
-    for I in graded_eachblockstoredindex(a)
-        c[I] = lazyblock(a, I)
-    end
-    return c
-end
-
-function TensorAlgebra.:+ₗ(a::LazyGradedArray, b::LazyGradedArray)
-    _check_add_axes(a, b)
-    return AddGradedArray(a, b)
-end
-TensorAlgebra.:*ₗ(α::Number, a::GradedArray) = ScaledGradedArray(α, a)
-TensorAlgebra.conjed(a::GradedArray) = ConjGradedArray(a)
-
-Base.copy(a::ScaledGradedArray) = copy_lazygraded(a)
-Base.copy(a::ConjGradedArray) = copy_lazygraded(a)
-Base.copy(a::AddGradedArray) = copy_lazygraded(a)
-Base.Array(a::ScaledGradedArray) = Array(copy(a))
-Base.Array(a::ConjGradedArray) = Array(copy(a))
-Base.Array(a::AddGradedArray) = Array(copy(a))
 
-function BC.broadcasted(style::GradedStyle, f, args...)
-    return TensorAlgebra.broadcasted_linear(style, f, args...)
+function Base.copyto!(dest::GradedArray, bc::BC.Broadcasted{<:GradedStyle})
+    lb = TensorAlgebra.tryflattenlinear(bc)
+    isnothing(lb) &&
+        throw(ArgumentError("GradedArray broadcasting requires linear operations"))
+    return copyto!(dest, lb)
 end
diff --git a/src/tensoralgebra.jl b/src/tensoralgebra.jl
index de7321e..475ded1 100644
--- a/src/tensoralgebra.jl
+++ b/src/tensoralgebra.jl
@@ -155,27 +155,34 @@ function TensorAlgebra.unmatricize(
     return SectorArray(msectors.sectors, mdata)
 end
 
-function TensorAlgebra.permutedimsadd!(
-        y::SectorArray, x::SectorArray, perm,
+function TensorAlgebra.permutedimsopadd!(
+        y::SectorArray, op, x::SectorArray, perm,
         α::Number, β::Number
     )
     ysectors, ydata = kroneckerfactors(y)
     xsectors, xdata = kroneckerfactors(x)
     ysectors == permutedims(xsectors, perm) || throw(DimensionMismatch())
     phase = fermion_permutation_phase(xsectors, perm)
-    TensorAlgebra.permutedimsadd!(ydata, xdata, perm, phase * α, β)
+    TensorAlgebra.permutedimsopadd!(ydata, op, xdata, perm, phase * α, β)
     return y
 end
-function TensorAlgebra.permutedimsadd!(
-        y::GradedArray{<:Any, N}, x::GradedArray{<:Any, N}, perm,
+function TensorAlgebra.permutedimsopadd!(
+        y::GradedArray{<:Any, N}, op, x::GradedArray{<:Any, N}, perm,
         α::Number, β::Number
     ) where {N}
-    y .*= β
+    if !iszero(β)
+        for bI in eachblockstoredindex(y)
+            y_b = @view!(y[bI])
+            idperm = ntuple(identity, ndims(y_b))
+            TensorAlgebra.permutedimsopadd!(y_b, identity, y_b, idperm, β, false)
+        end
+    end
     for bI in eachblockstoredindex(x)
         b = Tuple(bI)
-        b_dest = ntuple(i -> b[perm[i]], N)
-        y[Block(b_dest)] =
-            TensorAlgebra.permutedimsadd!(y[Block(b_dest)], x[bI], perm, α, true)
+        b_dest = Block(ntuple(i -> b[perm[i]], N))
+        y_b = @view!(y[b_dest])
+        x_b = @view!(x[bI])
+        TensorAlgebra.permutedimsopadd!(y_b, op, x_b, perm, α, true)
     end
     return y
 end
diff --git a/test/Project.toml b/test/Project.toml
index 5e8e370..fabe87c 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -30,13 +30,13 @@ ITensorPkgSkeleton = "0.3.42"
 KroneckerArrays = "0.3"
 LinearAlgebra = "1.10"
 MatrixAlgebraKit = "0.6"
-NamedDimsArrays = "0.13, 0.14"
+NamedDimsArrays = "0.15"
 Random = "1.10"
 SUNRepresentations = "0.3"
 SafeTestsets = "0.1"
 SparseArraysBase = "0.9"
 Suppressor = "0.2.8"
-TensorAlgebra = "0.7.19"
+TensorAlgebra = "0.8"
 TensorKitSectors = "0.3"
 Test = "1.10"
 TestExtras = "0.3.1"
diff --git a/test/test_gradedarray.jl b/test/test_gradedarray.jl
index f38968b..dcff3c5 100644
--- a/test/test_gradedarray.jl
+++ b/test/test_gradedarray.jl
@@ -9,7 +9,7 @@ using KroneckerArrays: cartesianrange
 using LinearAlgebra: adjoint
 using Random: randn!
 using SparseArraysBase: storedlength
-using TensorAlgebra: TensorAlgebra, *ₗ, +ₗ, -ₗ, /ₗ, conjed
+using TensorAlgebra: TensorAlgebra, linearbroadcasted
 using Test: @test, @test_broken, @test_throws, @testset
 
 function randn_blockdiagonal(elt::Type, axes::Tuple)
@@ -403,24 +403,28 @@ const elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
         @test Array(C) ≈ α .* Array(A) .+ β .* Array(B)
         @test axes(C) == axes(A)
         @test all(dim -> isdual(axes(C, dim)) == isdual(axes(A, dim)), 1:ndims(A))
-        Cₗ = α *ₗ A +ₗ β *ₗ B
+        Cₗ = linearbroadcasted(+, linearbroadcasted(*, α, A), linearbroadcasted(*, β, B))
         @test TensorAlgebra.iscall(Cₗ)
-        @test Array(Cₗ) ≈ α .* Array(A) .+ β .* Array(B)
+        @test Array(copy(Cₗ)) ≈ α .* Array(A) .+ β .* Array(B)
         @test axes(Cₗ) == axes(A)
 
         D = conj.(A) .- B ./ β
         @test Array(D) ≈ conj.(Array(A)) .- Array(B) ./ β
         @test axes(D) == axes(A)
-        Dₗ = conjed(A) -ₗ (B /ₗ β)
+        Dₗ = linearbroadcasted(
+            +,
+            linearbroadcasted(conj, A),
+            linearbroadcasted(*, -1 / β, B)
+        )
         @test TensorAlgebra.iscall(Dₗ)
-        @test Array(Dₗ) ≈ conj.(Array(A)) .- Array(B) ./ β
+        @test Array(copy(Dₗ)) ≈ conj.(Array(A)) .- Array(B) ./ β
         @test axes(Dₗ) == axes(A)
 
         @test_throws ArgumentError A .* B
 
         r_bad = gradedrange([U1(0) => 1, U1(1) => 3])
         B_bad = randn_blockdiagonal(elt, (r_bad, dual(r_bad)))
-        @test_throws ArgumentError A .+ B_bad
+        @test_throws DimensionMismatch A .+ B_bad
     end
     false && @testset "Construct from dense" begin
         r = gradedrange([U1(0) => 2, U1(1) => 3])
diff --git a/test/test_tensoralgebraext.jl b/test/test_tensoralgebraext.jl
index dd06702..04fe82f 100644
--- a/test/test_tensoralgebraext.jl
+++ b/test/test_tensoralgebraext.jl
@@ -4,8 +4,8 @@ using GradedArrays: GradedArray, GradedMatrix, SU2, SectorArray, SectorDelta, U1
     flip, gradedrange, isdual, sector, sector_type, sectorrange, trivial,
     trivial_gradedrange, ⊗
 using Random: randn!
-using TensorAlgebra: TensorAlgebra, *ₗ, +ₗ, -ₗ, /ₗ, FusionStyle, conjed, contract,
-    matricize, tensor_product_axis, trivial_axis, unmatricize
+using TensorAlgebra: TensorAlgebra, FusionStyle, contract, matricize, tensor_product_axis,
+    trivial_axis, unmatricize
 using Test: @test, @test_throws, @testset
 
 function randn_blockdiagonal(elt::Type, axes::Tuple)
@@ -76,38 +76,20 @@ end
     @test st.data isa Matrix
     @test Array(st) ≈ α .* Array(s) .+ β .* Array(t)
     @test axes(st) == axes(s)
-    @test (α *ₗ s) isa SectorArray
-    @test TensorAlgebra.iscall((α *ₗ s).data)
-    @test (α *ₗ s +ₗ β *ₗ t) isa SectorArray
-    @test TensorAlgebra.iscall((α *ₗ s +ₗ β *ₗ t).data)
-    @test Array(α *ₗ s +ₗ β *ₗ t) ≈ α .* Array(s) .+ β .* Array(t)
-    @test axes(α *ₗ s +ₗ β *ₗ t) == axes(s)
-    @test Base.broadcasted(*, α, s) isa SectorArray
-    @test TensorAlgebra.iscall(Base.broadcasted(*, α, s).data)
-
     conjdiff = conj.(s) .- t ./ β
     @test conjdiff isa SectorArray
     @test conjdiff.data isa Matrix
     @test Array(conjdiff) ≈ conj.(Array(s)) .- Array(t) ./ β
     @test axes(conjdiff) == axes(s)
-    @test conjed(s) isa SectorArray
-    @test TensorAlgebra.iscall(conjed(s).data)
-    @test (conjed(s) -ₗ (t /ₗ β)) isa SectorArray
-    @test TensorAlgebra.iscall((conjed(s) -ₗ (t /ₗ β)).data)
-    @test Array(conjed(s) -ₗ (t /ₗ β)) ≈ conj.(Array(s)) .- Array(t) ./ β
-    @test axes(conjed(s) -ₗ (t /ₗ β)) == axes(s)
 
     @test_throws ArgumentError s .* t
     @test_throws ArgumentError exp.(s)
 end
 
-@testset "SectorArray scalar multiplication materializes on broadcast materialize" begin
+@testset "SectorArray scalar multiplication materializes on broadcast" begin
     s = SectorArray((U1(0), dual(U1(0))), randn!(Matrix{Float64}(undef, 2, 2)))
 
-    scaled = Base.broadcasted(*, 2, s)
-    @test scaled isa SectorArray
-    @test TensorAlgebra.iscall(scaled.data)
-    materialized = Base.Broadcast.materialize(scaled)
+    materialized = 2 .* s
     @test materialized isa SectorArray
     @test materialized.data isa Matrix
     @test materialized[1, 1] == 2 * s[1, 1]
@@ -120,14 +102,6 @@ end
     @test Array(scaled_mul) ≈ 2 .* Array(s)
 end
 
-@testset "SectorArray lazy display" begin
-    s = SectorArray((U1(0), dual(U1(0))), randn!(Matrix{Float64}(undef, 2, 2)))
-    lazy = 2 *ₗ s
-    shown = sprint(show, MIME("text/plain"), lazy)
-    @test contains(shown, "SectorMatrix")
-    @test contains(shown, "⊗")
-end
-
 const elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
 @testset "`contract` `GradedArray` (eltype=$elt)" for elt in elts
     @testset "matricize" begin