diff --git a/Project.toml b/Project.toml
index 23fc5e15f..cad05b539 100644
--- a/Project.toml
+++ b/Project.toml
@@ -34,7 +34,7 @@ HalfIntegers = "1.6.0"
 KrylovKit = "0.8.3, 0.9.2, 0.10"
 LinearAlgebra = "1.6"
 LoggingExtras = "~1.0"
-MatrixAlgebraKit = "0.5.0"
+MatrixAlgebraKit = "0.6.0"
 OhMyThreads = "0.7, 0.8"
 OptimKit = "0.3.1, 0.4"
 Pkg = "1"
@@ -42,7 +42,7 @@ Plots = "1.40"
 Printf = "1"
 Random = "1"
 RecipesBase = "1.1"
-TensorKit = "0.15.1"
+TensorKit = "0.16.0"
 TensorKitManifolds = "0.7"
 TensorOperations = "5"
 Test = "1"
@@ -60,3 +60,6 @@ TestExtras = "5ed8adda-3752-4e41-b88a-e8b09835ee3a"
 
 [targets]
 test = ["Aqua", "Pkg", "Test", "TestExtras", "Plots", "Combinatorics"]
+
+[sources]
+TensorKitManifolds = {url="https://github.com/Jutho/TensorKitManifolds.jl", rev="main"}
diff --git a/src/utility/utility.jl b/src/utility/utility.jl
index 418e0cd68..d33b2c7ec 100644
--- a/src/utility/utility.jl
+++ b/src/utility/utility.jl
@@ -153,26 +153,34 @@ end
 # temporary workaround for the fact that left_orth and right_orth are poorly designed:
 function _left_orth!(t; alg::MatrixAlgebraKit.AbstractAlgorithm, trunc::MatrixAlgebraKit.TruncationStrategy = notrunc())
     if alg isa LAPACK_HouseholderQR
-        return left_orth!(t; kind = :qr, alg_qr = alg, trunc)
+        left_orth_alg = MatrixAlgebraKit.select_algorithm(left_orth!, t, Val(:qr); alg.kwargs...)
+        return left_orth!(t, left_orth_alg)
     elseif alg isa LAPACK_HouseholderLQ
-        return left_orth!(t; kind = :qr, alg_qr = LAPACK_HouseholderQR(; alg.kwargs...), trunc)
+        left_orth_alg = MatrixAlgebraKit.select_algorithm(left_orth!, t, Val(:qr); alg.kwargs...)
+        return left_orth!(t, left_orth_alg)
     elseif alg isa PolarViaSVD
-        return left_orth!(t; kind = :polar, alg_polar = alg, trunc)
+        left_orth_alg = MatrixAlgebraKit.select_algorithm(left_orth!, t, Val(:polar); alg.kwargs...)
+        return left_orth!(t, left_orth_alg)
     elseif alg isa LAPACK_SVDAlgorithm
-        return left_orth!(t; kind = :svd, alg_svd = alg, trunc)
+        left_orth_alg = MatrixAlgebraKit.select_algorithm(left_orth!, t, Val(:svd); trunc, alg.kwargs...)
+        return left_orth!(t, left_orth_alg)
     else
         error(lazy"unkown algorithm $alg")
     end
 end
 function _right_orth!(t; alg::MatrixAlgebraKit.AbstractAlgorithm, trunc::TruncationStrategy = notrunc())
     if alg isa LAPACK_HouseholderLQ
-        return right_orth!(t; kind = :lq, alg_lq = alg, trunc)
+        right_orth_alg = MatrixAlgebraKit.select_algorithm(right_orth!, t, Val(:lq); alg.kwargs...)
+        return right_orth!(t, right_orth_alg)
     elseif alg isa LAPACK_HouseholderQR
-        return right_orth!(t; kind = :lq, alg_lq = LAPACK_HouseholderLQ(; alg.kwargs...), trunc)
+        right_orth_alg = MatrixAlgebraKit.select_algorithm(right_orth!, t, Val(:lq); alg.kwargs...)
+        return right_orth!(t, right_orth_alg)
     elseif alg isa PolarViaSVD
-        return right_orth!(t; kind = :polar, alg_polar = alg, trunc)
+        right_orth_alg = MatrixAlgebraKit.select_algorithm(right_orth!, t, Val(:polar); alg.kwargs...)
+        return right_orth!(t, right_orth_alg)
     elseif alg isa LAPACK_SVDAlgorithm
-        return right_orth!(t; kind = :svd, alg_svd = alg, trunc)
+        right_orth_alg = MatrixAlgebraKit.select_algorithm(right_orth!, t, Val(:svd); trunc, alg.kwargs...)
+        return right_orth!(t, right_orth_alg)
     else
         error(lazy"unkown algorithm $alg")
     end