Formatting changes

lkdvos · lkdvos · commit 8133147b5b73 · 2025-06-30T12:53:25.000+02:00
diff --git a/examples/classic2d/1.hard-hexagon/main.jl b/examples/classic2d/1.hard-hexagon/main.jl
@@ -39,10 +39,10 @@ Additionally, we can compute the entanglement entropy as well as the correlation
 D = 10
 V = virtual_space(D)
 ψ₀ = InfiniteMPS([P], [V])
-ψ, envs, = leading_boundary(ψ₀, mpo,
-                            VUMPS(; verbosity=0,
-                                  alg_eigsolve=MPSKit.Defaults.alg_eigsolve(;
-                                                                            ishermitian=false))) # use non-hermitian eigensolver
+ψ, envs = leading_boundary(ψ₀, mpo,
+                           VUMPS(; verbosity=0,
+                                 alg_eigsolve=MPSKit.Defaults.alg_eigsolve(;
+                                                                           ishermitian=false))) # use non-hermitian eigensolver
 F = real(expectation_value(ψ, mpo))
 S = real(first(entropy(ψ)))
 ξ = correlation_length(ψ)
@@ -63,13 +63,13 @@ function scaling_simulations(ψ₀, mpo, Ds; verbosity=0, tol=1e-6,
     correlations = similar(Ds, Float64)
     alg = VUMPS(; verbosity, tol, alg_eigsolve)
 
-    ψ, envs, = leading_boundary(ψ₀, mpo, alg)
+    ψ, envs = leading_boundary(ψ₀, mpo, alg)
     entropies[1] = real(entropy(ψ)[1])
     correlations[1] = correlation_length(ψ)
 
     for (i, d) in enumerate(diff(Ds))
         ψ, envs = changebonds(ψ, mpo, OptimalExpand(; trscheme=truncdim(d)), envs)
-        ψ, envs, = leading_boundary(ψ, mpo, alg, envs)
+        ψ, envs = leading_boundary(ψ, mpo, alg, envs)
         entropies[i + 1] = real(entropy(ψ)[1])
         correlations[i + 1] = correlation_length(ψ)
     end
diff --git a/examples/quantum1d/7.xy-finiteT/main.jl b/examples/quantum1d/7.xy-finiteT/main.jl
@@ -29,7 +29,7 @@ J = 1 / 2
 T = ComplexF64
 symmetry = U1Irrep
 
-function XY_hamiltonian(::Type{T}=ComplexF64, ::Type{S}=Trivial; J=1 / 2,
+function XY_hamiltonian((::Type{T})=ComplexF64, (::Type{S})=Trivial; J=1 / 2,
                         N) where {T<:Number,S<:Sector}
     spin = 1 // 2
     term = J * (S_xx(T, S; spin) + S_yy(T, S; spin))
@@ -90,7 +90,7 @@ D = 64
 V_init = symmetry === Trivial ? ℂ^32 : U1Space(i => 10 for i in -1:(1 // 2):1)
 psi_init = FiniteMPS(N, physicalspace(H, 1), V_init)
 trscheme = truncdim(D)
-psi, envs, = find_groundstate(psi_init, H, DMRG2(; trscheme, maxiter=5));
+psi, envs = find_groundstate(psi_init, H, DMRG2(; trscheme, maxiter=5));
 E_0 = expectation_value(psi, H, envs) / N
 
 println("Numerical:\t", real(E_0))
diff --git a/src/algorithms/approximate/fvomps.jl b/src/algorithms/approximate/fvomps.jl
@@ -9,7 +9,7 @@ function approximate!(ψ::AbstractFiniteMPS, Oϕ, alg::DMRG2,
             ϵ = 0.0
             for pos in [1:(length(ψ) - 1); (length(ψ) - 2):-1:1]
                 AC2′ = AC2_projection(pos, ψ, Oϕ, envs)
-                al, c, ar, = tsvd!(AC2′; trunc=alg.trscheme)
+                al, c, ar = tsvd!(AC2′; trunc=alg.trscheme)
 
                 AC2 = ψ.AC[pos] * _transpose_tail(ψ.AR[pos + 1])
                 ϵ = max(ϵ, norm(al * c * ar - AC2) / norm(AC2))
diff --git a/src/algorithms/changebonds/optimalexpand.jl b/src/algorithms/changebonds/optimalexpand.jl
@@ -31,7 +31,7 @@ function changebonds(ψ::InfiniteMPS, H::InfiniteMPOHamiltonian, alg::OptimalExp
         VL = leftnull(ψ.AL[i])
         VR = rightnull!(_transpose_tail(ψ.AR[i + 1]))
         intermediate = normalize!(adjoint(VL) * AC2 * adjoint(VR))
-        U, _, V, = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, _, V = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
 
         AL′[i] = VL * U
         AR′[i + 1] = V * VR
@@ -57,7 +57,7 @@ function changebonds(ψ::MultilineMPS, H, alg::OptimalExpand, envs=environments(
         VL = leftnull(ψ.AL[i, j])
         VR = rightnull!(_transpose_tail(ψ.AR[i, j + 1]))
         intermediate = normalize!(adjoint(VL) * AC2 * adjoint(VR))
-        U, _, V, = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, _, V = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
 
         AL′[i, j] = VL * U
         AR′[i, j + 1] = V * VR
@@ -88,7 +88,7 @@ function changebonds!(ψ::AbstractFiniteMPS, H, alg::OptimalExpand, envs=environ
 
         #Use this nullspaces and SVD decomposition to determine the optimal expansion space
         intermediate = normalize!(adjoint(NL) * AC2 * adjoint(NR))
-        _, _, V, = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
+        _, _, V = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
 
         ar_re = V * NR
         ar_le = zerovector!(similar(ar_re, codomain(ψ.AC[i]) ← space(V, 1)))
diff --git a/src/algorithms/changebonds/randexpand.jl b/src/algorithms/changebonds/randexpand.jl
@@ -29,7 +29,7 @@ function changebonds(ψ::InfiniteMPS, alg::RandExpand)
         VL = leftnull(ψ.AL[i])
         VR = rightnull!(_transpose_tail(ψ.AR[i + 1]))
         intermediate = normalize!(adjoint(VL) * AC2 * adjoint(VR))
-        U, _, V, = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, _, V = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
 
         AL′[i] = VL * U
         AR′[i + 1] = V * VR
@@ -53,7 +53,7 @@ function changebonds!(ψ::AbstractFiniteMPS, alg::RandExpand)
 
         #Use this nullspaces and SVD decomposition to determine the optimal expansion space
         intermediate = normalize!(adjoint(NL) * AC2 * adjoint(NR))
-        _, _, V, = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
+        _, _, V = tsvd!(intermediate; trunc=alg.trscheme, alg=alg.alg_svd)
 
         ar_re = V * NR
         ar_le = zerovector!(similar(ar_re, codomain(ψ.AC[i]) ← space(V, 1)))
diff --git a/src/algorithms/changebonds/svdcut.jl b/src/algorithms/changebonds/svdcut.jl
@@ -20,7 +20,7 @@ function changebonds(ψ::AbstractFiniteMPS, alg::SvdCut; kwargs...)
 end
 function changebonds!(ψ::AbstractFiniteMPS, alg::SvdCut; normalize::Bool=true)
     for i in (length(ψ) - 1):-1:1
-        U, S, V, = tsvd(ψ.C[i]; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, S, V = tsvd(ψ.C[i]; trunc=alg.trscheme, alg=alg.alg_svd)
         AL′ = ψ.AL[i] * U
         ψ.AC[i] = (AL′, complex(S))
         AR′ = _transpose_front(V * _transpose_tail(ψ.AR[i + 1]))
@@ -44,7 +44,7 @@ function changebonds!(mpo::FiniteMPO, alg::SvdCut)
     O_left = transpose(mpo[1], ((3, 1, 2), (4,)))
     local O_right
     for i in 2:length(mpo)
-        U, S, V, = tsvd!(O_left; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, S, V = tsvd!(O_left; trunc=alg.trscheme, alg=alg.alg_svd)
         @inbounds mpo[i - 1] = transpose(U, ((2, 3), (1, 4)))
         if i < length(mpo)
             @plansor O_left[-3 -1 -2; -4] := S[-1; 1] * V[1; 2] * mpo[i][2 -2; -3 -4]
@@ -55,7 +55,7 @@ function changebonds!(mpo::FiniteMPO, alg::SvdCut)
 
     # right to left
     for i in (length(mpo) - 1):-1:1
-        U, S, V, = tsvd!(O_right; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, S, V = tsvd!(O_right; trunc=alg.trscheme, alg=alg.alg_svd)
         @inbounds mpo[i + 1] = transpose(V, ((1, 4), (2, 3)))
         if i > 1
             @plansor O_right[-1; -3 -4 -2] := mpo[i][-1 -2; -3 2] * U[2; 1] * S[1; -4]
@@ -84,7 +84,7 @@ function changebonds(ψ::InfiniteMPS, alg::SvdCut)
     ncr = ψ.C[1]
 
     for i in 1:length(ψ)
-        U, ncr, = tsvd(ψ.C[i]; trunc=alg.trscheme, alg=alg.alg_svd)
+        U, ncr = tsvd(ψ.C[i]; trunc=alg.trscheme, alg=alg.alg_svd)
         copied[i] = copied[i] * U
         copied[i + 1] = _transpose_front(U' * _transpose_tail(copied[i + 1]))
     end
diff --git a/src/algorithms/excitation/chepigaansatz.jl b/src/algorithms/excitation/chepigaansatz.jl
@@ -117,7 +117,7 @@ function excitations(H, alg::ChepigaAnsatz2, ψ::FiniteMPS, envs=environments(ψ
     # map back to finitemps
     ψs = map(AC2s) do ac
         ψ′ = copy(ψ)
-        AL, C, AR, = tsvd!(ac; trunc=alg.trscheme)
+        AL, C, AR = tsvd!(ac; trunc=alg.trscheme)
         normalize!(C)
         ψ′.AC[pos] = (AL, complex(C))
         ψ′.AC[pos + 1] = (complex(C), _transpose_front(AR))
diff --git a/src/algorithms/groundstate/dmrg.jl b/src/algorithms/groundstate/dmrg.jl
@@ -121,7 +121,7 @@ function find_groundstate!(ψ::AbstractFiniteMPS, H, alg::DMRG2, envs=environmen
                 Hac2 = AC2_hamiltonian(pos, ψ, H, ψ, envs)
                 _, newA2center = fixedpoint(Hac2, ac2, :SR, alg_eigsolve)
 
-                al, c, ar, = tsvd!(newA2center; trunc=alg.trscheme, alg=alg.alg_svd)
+                al, c, ar = tsvd!(newA2center; trunc=alg.trscheme, alg=alg.alg_svd)
                 normalize!(c)
                 v = @plansor ac2[1 2; 3 4] * conj(al[1 2; 5]) * conj(c[5; 6]) *
                              conj(ar[6; 3 4])
@@ -137,7 +137,7 @@ function find_groundstate!(ψ::AbstractFiniteMPS, H, alg::DMRG2, envs=environmen
                 Hac2 = AC2_hamiltonian(pos, ψ, H, ψ, envs)
                 _, newA2center = fixedpoint(Hac2, ac2, :SR, alg_eigsolve)
 
-                al, c, ar, = tsvd!(newA2center; trunc=alg.trscheme, alg=alg.alg_svd)
+                al, c, ar = tsvd!(newA2center; trunc=alg.trscheme, alg=alg.alg_svd)
                 normalize!(c)
                 v = @plansor ac2[1 2; 3 4] * conj(al[1 2; 5]) * conj(c[5; 6]) *
                              conj(ar[6; 3 4])
diff --git a/src/algorithms/groundstate/gradient_grassmann.jl b/src/algorithms/groundstate/gradient_grassmann.jl
@@ -34,7 +34,7 @@ struct GradientGrassmann{O<:OptimKit.OptimizationAlgorithm,F} <: Algorithm
 
     function GradientGrassmann(; method=ConjugateGradient, (finalize!)=OptimKit._finalize!,
                                tol=Defaults.tol, maxiter=Defaults.maxiter,
-                               verbosity=Defaults.verbosity - 1)
+                               verbosity=(Defaults.verbosity - 1))
         if isa(method, OptimKit.OptimizationAlgorithm)
             # We were given an optimisation method, just use it.
             m = method
diff --git a/src/algorithms/groundstate/idmrg.jl b/src/algorithms/groundstate/idmrg.jl
@@ -133,7 +133,7 @@ function find_groundstate(ost::InfiniteMPS, H, alg::IDMRG2, envs=environments(os
                 h_ac2 = AC2_hamiltonian(pos, ψ, H, ψ, envs)
                 _, ac2′ = fixedpoint(h_ac2, ac2, :SR, alg_eigsolve)
 
-                al, c, ar, = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
+                al, c, ar = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
                 normalize!(c)
 
                 ψ.AL[pos] = al
@@ -152,7 +152,7 @@ function find_groundstate(ost::InfiniteMPS, H, alg::IDMRG2, envs=environments(os
             h_ac2 = AC2_hamiltonian(0, ψ, H, ψ, envs)
             _, ac2′ = fixedpoint(h_ac2, ac2, :SR, alg_eigsolve)
 
-            al, c, ar, = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
+            al, c, ar = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
             normalize!(c)
 
             ψ.AL[end] = al
@@ -175,7 +175,7 @@ function find_groundstate(ost::InfiniteMPS, H, alg::IDMRG2, envs=environments(os
                 h_ac2 = AC2_hamiltonian(pos, ψ, H, ψ, envs)
                 _, ac2′ = fixedpoint(h_ac2, ac2, :SR, alg_eigsolve)
 
-                al, c, ar, = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
+                al, c, ar = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
                 normalize!(c)
 
                 ψ.AL[pos] = al
@@ -194,7 +194,7 @@ function find_groundstate(ost::InfiniteMPS, H, alg::IDMRG2, envs=environments(os
             ac2 = AC2(ψ, 0; kind=:ACAR)
             h_ac2 = AC2_hamiltonian(0, ψ, H, ψ, envs)
             _, ac2′ = fixedpoint(h_ac2, ac2, :SR, alg_eigsolve)
-            al, c, ar, = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
+            al, c, ar = tsvd!(ac2′; trunc=alg.trscheme, alg=alg.alg_svd)
             normalize!(c)
 
             ψ.AL[end] = al
diff --git a/src/algorithms/toolbox.jl b/src/algorithms/toolbox.jl
@@ -119,7 +119,7 @@ Find the closest fractions of π, differing at most ```tol_angle```
 """
 function approx_angles(spectrum; tol_angle=0.1)
     angles = angle.(spectrum) ./ π                          # ∈ ]-1, 1]
-    angles_approx = rationalize.(angles, tol=tol_angle)     # ∈ [-1, 1]
+    angles_approx = rationalize.(angles; tol=tol_angle)     # ∈ [-1, 1]
 
     # Remove the effects of the branchcut.
     angles_approx[findall(angles_approx .== -1)] .= 1       # ∈ ]-1, 1]
diff --git a/src/environments/qp_envs.jl b/src/environments/qp_envs.jl
@@ -100,10 +100,10 @@ function environments(exci::InfiniteQP, H::InfiniteMPOHamiltonian,
 
     @sync begin
         Threads.@spawn $lBs[1] = left_excitation_transfer_system($lBs[1], $H, $exci;
-                                                                 solver=$solver)
+                                                                 solver=($solver))
         Threads.@spawn $rBs[end] = right_excitation_transfer_system($rBs[end], $H,
                                                                     $exci;
-                                                                    solver=$solver)
+                                                                    solver=($solver))
     end
 
     lB_cur = lBs[1]
diff --git a/src/states/infinitemps.jl b/src/states/infinitemps.jl
@@ -89,11 +89,11 @@ struct InfiniteMPS{A<:GenericMPSTensor,B<:MPSBondTensor} <: AbstractMPS
 
             # verify that the virtual spaces are compatible
             space(AL[i], 1) == dual(space(AL[i - 1], N)) &&
-                space(AR[i], 1) == dual(space(AR[i - 1], N)) &&
-                space(AC[i], 1) == space(AL[i], 1) &&
-                space(AC[i], N) == space(AR[i], N) &&
-                space(C[i], 1) == dual(space(AL[i], N)) &&
-                space(AR[i], 1) == dual(space(C[i - 1], 2)) ||
+            space(AR[i], 1) == dual(space(AR[i - 1], N)) &&
+            space(AC[i], 1) == space(AL[i], 1) &&
+            space(AC[i], N) == space(AR[i], N) &&
+            space(C[i], 1) == dual(space(AL[i], N)) &&
+            space(AR[i], 1) == dual(space(C[i - 1], 2)) ||
                 throw(SpaceMismatch("incompatible virtual spaces at site $i"))
             # verify that the spaces are non-zero
             dim(space(AL[i])) > 0 && dim(space(C[i])) > 0 ||
diff --git a/src/states/quasiparticle_state.jl b/src/states/quasiparticle_state.jl
@@ -80,10 +80,10 @@ function RightGaugedQP(datfun, left_gs, right_gs=left_gs;
 end
 
 #gauge dependent code
-function Base.similar(v::LeftGaugedQP, ::Type{T}=scalartype(v)) where {T<:Number}
+function Base.similar(v::LeftGaugedQP, (::Type{T})=scalartype(v)) where {T<:Number}
     return LeftGaugedQP(v.left_gs, v.right_gs, v.VLs, similar.(v.Xs, T), v.momentum)
 end
-function Base.similar(v::RightGaugedQP, ::Type{T}=scalartype(v)) where {T<:Number}
+function Base.similar(v::RightGaugedQP, (::Type{T})=scalartype(v)) where {T<:Number}
     return RightGaugedQP(v.left_gs, v.right_gs, similar.(v.Xs, T), v.VRs, v.momentum)
 end
 
diff --git a/src/states/windowmps.jl b/src/states/windowmps.jl
@@ -44,7 +44,7 @@ struct WindowMPS{A<:GenericMPSTensor,B<:MPSBondTensor} <: AbstractFiniteMPS
                        ψᵣ::InfiniteMPS{A,B}=copy(ψₗ)) where {A<:GenericMPSTensor,
                                                              B<:MPSBondTensor}
         left_virtualspace(ψₗ, 1) == left_virtualspace(ψₘ, 1) &&
-            right_virtualspace(ψₘ, length(ψₘ)) == right_virtualspace(ψᵣ, length(ψₘ)) ||
+        right_virtualspace(ψₘ, length(ψₘ)) == right_virtualspace(ψᵣ, length(ψₘ)) ||
             throw(SpaceMismatch("Mismatch between window and environment virtual spaces"))
         return new{A,B}(ψₗ, ψₘ, ψᵣ)
     end
diff --git a/test/algorithms.jl b/test/algorithms.jl
@@ -351,6 +351,7 @@ end
 
     @testset "Finite TimeDependent LazySum $(alg isa TDVP ? "TDVP" : "TDVP2")" for alg in
                                                                                    algs
+
         ψ, envs = timestep(ψ₀, Ht(1.0), 0.0, dt, alg)
         E = expectation_value(ψ, Ht(1.0), envs)
 
@@ -363,6 +364,7 @@ end
           MultipliedOperator(H, 1.45)
     @testset "Finite TimeDependent LazySum (fix negative t issue) $(alg isa TDVP ? "TDVP" : "TDVP2")" for alg in
                                                                                                           algs
+
         ψ, envs = timestep(ψ₀, Ht2, 0.0, dt, alg)
         E = expectation_value(ψ, Ht2(0.0), envs)
 
@@ -489,7 +491,7 @@ end
         fin_en = map([20, 10]) do len
             H = force_planar(transverse_field_ising(; L=len))
             ψ = FiniteMPS(rand, ComplexF64, len, ℙ^2, ℙ^10)
-            ψ, envs, = find_groundstate(ψ, H; verbosity)
+            ψ, envs = find_groundstate(ψ, H; verbosity)
 
             # find energy with quasiparticle ansatz
             energies_QP, ϕs = @inferred excitations(H, QuasiparticleAnsatz(), ψ, envs)
@@ -658,7 +660,7 @@ end
     for λ in [1.05, 2.0, 4.0]
         H = hamiltonian(λ)
         ψ = InfiniteMPS([ℂ^2], [ℂ^16])
-        ψ, envs, = find_groundstate(ψ, H, VUMPS(; maxiter=100, verbosity=0))
+        ψ, envs = find_groundstate(ψ, H, VUMPS(; maxiter=100, verbosity=0))
 
         numerical_susceptibility = fidelity_susceptibility(ψ, H, [H_X], envs; maxiter=10)
         @test numerical_susceptibility[1, 1] ≈ analytical_susceptibility(λ) atol = 1e-2
@@ -668,7 +670,7 @@ end
             Hfin = open_boundary_conditions(hamiltonian(λ), L)
             H_Xfin = open_boundary_conditions(H_X, L)
             ψ = FiniteMPS(rand, ComplexF64, L, ℂ^2, ℂ^16)
-            ψ, envs, = find_groundstate(ψ, Hfin, DMRG(; verbosity=0))
+            ψ, envs = find_groundstate(ψ, Hfin, DMRG(; verbosity=0))
             numerical_susceptibility = fidelity_susceptibility(ψ, Hfin, [H_Xfin], envs;
                                                                maxiter=10)
             return numerical_susceptibility[1, 1] / L
diff --git a/test/setup.jl b/test/setup.jl
@@ -86,7 +86,8 @@ end
 # Toy models
 # ----------------------------
 
-function S_x(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_x((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+             spin=1 // 2) where {T<:Number}
     return if spin == 1 // 2
         TensorMap(T[0 1; 1 0], ℂ^2 ← ℂ^2)
     elseif spin == 1
@@ -95,7 +96,8 @@ function S_x(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {
         throw(ArgumentError("spin $spin not supported"))
     end
 end
-function S_y(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_y((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+             spin=1 // 2) where {T<:Number}
     return if spin == 1 // 2
         TensorMap(T[0 -im; im 0], ℂ^2 ← ℂ^2)
     elseif spin == 1
@@ -104,7 +106,8 @@ function S_y(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {
         throw(ArgumentError("spin $spin not supported"))
     end
 end
-function S_z(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_z((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+             spin=1 // 2) where {T<:Number}
     return if spin == 1 // 2
         TensorMap(T[1 0; 0 -1], ℂ^2 ← ℂ^2)
     elseif spin == 1
@@ -113,17 +116,20 @@ function S_z(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {
         throw(ArgumentError("spin $spin not supported"))
     end
 end
-function S_xx(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_xx((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+              spin=1 // 2) where {T<:Number}
     return S_x(Trivial, T; spin) ⊗ S_x(Trivial, T; spin)
 end
-function S_yy(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_yy((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+              spin=1 // 2) where {T<:Number}
     return S_y(Trivial, T; spin) ⊗ S_y(Trivial, T; spin)
 end
-function S_zz(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1 // 2) where {T<:Number}
+function S_zz((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64;
+              spin=1 // 2) where {T<:Number}
     return S_z(Trivial, T; spin) ⊗ S_z(Trivial, T; spin)
 end
 
-function transverse_field_ising(::Type{T}=ComplexF64; g=1.0, L=Inf) where {T<:Number}
+function transverse_field_ising((::Type{T})=ComplexF64; g=1.0, L=Inf) where {T<:Number}
     X = S_x(Trivial, T; spin=1 // 2)
     ZZ = S_zz(Trivial, T; spin=1 // 2)
 
@@ -156,7 +162,7 @@ function heisenberg_XXX(::Type{SU2Irrep}; spin=1, L=Inf)
     end
 end
 
-function heisenberg_XXX(::Type{Trivial}=Trivial, ::Type{T}=ComplexF64; spin=1,
+function heisenberg_XXX((::Type{Trivial})=Trivial, (::Type{T})=ComplexF64; spin=1,
                         L=Inf) where {T<:Number}
     h = ones(T, SU2Space(spin => 1)^2 ← SU2Space(spin => 1)^2)
     for (c, b) in blocks(h)
