diff --git a/Manifest.toml b/Manifest.toml
index 9fc0409..e12086f 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -1,8 +1,8 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.11.2"
+julia_version = "1.10.5"
 manifest_format = "2.0"
-project_hash = "a11849c16b8a292508a1917ef28e3146642e2d77"
+project_hash = "a23e703e9eb4627d34909a54a62cb3e99c92aa51"
 
 [[deps.AbstractTrees]]
 git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
@@ -57,7 +57,7 @@ version = "2.4.0"
 
 [[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
-version = "1.1.2"
+version = "1.1.1"
 
 [[deps.ArnoldiMethod]]
 deps = ["LinearAlgebra", "Random", "StaticArrays"]
@@ -109,7 +109,6 @@ weakdeps = ["SparseArrays"]
 
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
-version = "1.11.0"
 
 [[deps.AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
@@ -141,7 +140,6 @@ version = "0.4.3"
 
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
-version = "1.11.0"
 
 [[deps.Baselet]]
 git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
@@ -181,13 +179,13 @@ version = "0.7.3"
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Lz4_jll", "Zlib_jll", "Zstd_jll"]
 git-tree-sha1 = "ef12cdd1c7fb7e1dfd6fa8fd60d4db6bc61d2f23"
 uuid = "0b7ba130-8d10-5ba8-a3d6-c5182647fed9"
-version = "1.21.6+0"
+version = "1.21.6+2"
 
 [[deps.Bzip2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "8873e196c2eb87962a2048b3b8e08946535864a1"
 uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
-version = "1.0.8+2"
+version = "1.0.8+4"
 
 [[deps.Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
@@ -197,9 +195,9 @@ version = "1.18.2+1"
 
 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra"]
-git-tree-sha1 = "3e4b134270b372f2ed4d4d0e936aabaefc1802bc"
+git-tree-sha1 = "1713c74e00545bfe14605d2a2be1712de8fbcb58"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.25.0"
+version = "1.25.1"
 weakdeps = ["SparseArrays"]
 
     [deps.ChainRulesCore.extensions]
@@ -313,7 +311,6 @@ version = "1.0.0"
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
-version = "1.11.0"
 
 [[deps.Dbus_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"]
@@ -341,7 +338,6 @@ version = "0.4.3"
 [[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
-version = "1.11.0"
 
 [[deps.DocStringExtensions]]
 deps = ["LibGit2"]
@@ -382,7 +378,7 @@ version = "0.1.11"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "e51db81749b0777b2147fbe7b783ee79045b8e99"
 uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
-version = "2.6.4+1"
+version = "2.6.4+3"
 
 [[deps.ExprTools]]
 git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
@@ -423,7 +419,6 @@ weakdeps = ["HTTP"]
 
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
-version = "1.11.0"
 
 [[deps.FillArrays]]
 deps = ["LinearAlgebra"]
@@ -478,9 +473,9 @@ version = "2.13.3+1"
 
 [[deps.FriBidi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2"
+git-tree-sha1 = "846f7026a9decf3679419122b49f8a1fdb48d2d5"
 uuid = "559328eb-81f9-559d-9380-de523a88c83c"
-version = "1.0.14+0"
+version = "1.0.16+0"
 
 [[deps.Functors]]
 deps = ["Compat", "ConstructionBase", "LinearAlgebra", "Random"]
@@ -491,25 +486,24 @@ version = "0.5.2"
 [[deps.Future]]
 deps = ["Random"]
 uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
-version = "1.11.0"
 
 [[deps.GLFW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"]
-git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077"
+git-tree-sha1 = "fcb0584ff34e25155876418979d4c8971243bb89"
 uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
-version = "3.4.0+1"
+version = "3.4.0+2"
 
 [[deps.GR]]
 deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
-git-tree-sha1 = "52adc6828958ea8a0cf923d53aa10773dbca7d5f"
+git-tree-sha1 = "424c8f76017e39fdfcdbb5935a8e6742244959e8"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.73.9"
+version = "0.73.10"
 
 [[deps.GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "4e9e2966af45b06f24fd952285841428f1d6e858"
+git-tree-sha1 = "b90934c8cb33920a8dc66736471dc3961b42ec9f"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.73.9+0"
+version = "0.73.10+0"
 
 [[deps.GeoFormatTypes]]
 git-tree-sha1 = "59107c179a586f0fe667024c5eb7033e81333271"
@@ -542,9 +536,9 @@ version = "0.21.0+0"
 
 [[deps.Glib_jll]]
 deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
-git-tree-sha1 = "48b5d4c75b2c9078ead62e345966fa51a25c05ad"
+git-tree-sha1 = "b0036b392358c80d2d2124746c2bf3d48d457938"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
-version = "2.82.2+1"
+version = "2.82.4+0"
 
 [[deps.GraphRecipes]]
 deps = ["AbstractTrees", "GeometryTypes", "Graphs", "InteractiveUtils", "Interpolations", "LinearAlgebra", "NaNMath", "NetworkLayout", "PlotUtils", "RecipesBase", "SparseArrays", "Statistics"]
@@ -595,9 +589,9 @@ version = "1.14.2+1"
 
 [[deps.HTTP]]
 deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "PrecompileTools", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
-git-tree-sha1 = "627fcacdb7cb51dc67f557e1598cdffe4dda386d"
+git-tree-sha1 = "c67b33b085f6e2faf8bf79a61962e7339a81129c"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "1.10.14"
+version = "1.10.15"
 
 [[deps.HalfIntegers]]
 git-tree-sha1 = "9c3149243abb5bc0bad0431d6c4fcac0f4443c7c"
@@ -614,7 +608,7 @@ version = "8.5.0+0"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "50aedf345a709ab75872f80a2779568dc0bb461b"
 uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
-version = "2.11.2+1"
+version = "2.11.2+3"
 
 [[deps.ITensorMPS]]
 deps = ["Adapt", "Compat", "ITensors", "IsApprox", "KrylovKit", "LinearAlgebra", "NDTensors", "Printf", "Random", "SerializedElementArrays", "TupleTools"]
@@ -688,7 +682,6 @@ version = "1.4.2"
 [[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
-version = "1.11.0"
 
 [[deps.Interpolations]]
 deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
@@ -745,9 +738,9 @@ version = "0.1.9"
 
 [[deps.JLLWrappers]]
 deps = ["Artifacts", "Preferences"]
-git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b"
+git-tree-sha1 = "a007feb38b422fbdab534406aeca1b86823cb4d6"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.6.1"
+version = "1.7.0"
 
 [[deps.JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
@@ -763,9 +756,9 @@ version = "0.7.0"
 
 [[deps.JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c"
+git-tree-sha1 = "eac1206917768cb54957c65a615460d87b455fc1"
 uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
-version = "3.0.4+0"
+version = "3.1.1+0"
 
 [[deps.KrylovKit]]
 deps = ["LinearAlgebra", "PackageExtensionCompat", "Printf", "Random", "VectorInterface"]
@@ -785,9 +778,9 @@ version = "3.100.2+0"
 
 [[deps.LERC_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "36bdbc52f13a7d1dcb0f3cd694e01677a515655b"
+git-tree-sha1 = "aaafe88dccbd957a8d82f7d05be9b69172e0cee3"
 uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
-version = "4.0.0+0"
+version = "4.0.1+0"
 
 [[deps.LLVMOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -808,7 +801,7 @@ weakdeps = ["Serialization"]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731"
 uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
-version = "2.10.2+1"
+version = "2.10.2+3"
 
 [[deps.LaTeXStrings]]
 git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c"
@@ -834,7 +827,6 @@ version = "0.16.5"
 [[deps.LazyArtifacts]]
 deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
-version = "1.11.0"
 
 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
@@ -844,17 +836,16 @@ version = "0.6.4"
 [[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
-version = "8.6.0+0"
+version = "8.4.0+0"
 
 [[deps.LibGit2]]
 deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
-version = "1.11.0"
 
 [[deps.LibGit2_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
 uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
-version = "1.7.2+0"
+version = "1.6.4+0"
 
 [[deps.LibSSH2_jll]]
 deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
@@ -863,13 +854,12 @@ version = "1.11.0+1"
 
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
-version = "1.11.0"
 
 [[deps.Libffi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
+git-tree-sha1 = "27ecae93dd25ee0909666e6835051dd684cc035e"
 uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
-version = "3.2.2+1"
+version = "3.2.2+2"
 
 [[deps.Libgcrypt_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"]
@@ -885,9 +875,9 @@ version = "1.7.0+0"
 
 [[deps.Libgpg_error_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "c6ce1e19f3aec9b59186bdf06cdf3c4fc5f5f3e6"
+git-tree-sha1 = "df37206100d39f79b3376afb6b9cee4970041c61"
 uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
-version = "1.50.0+0"
+version = "1.51.1+0"
 
 [[deps.Libiconv_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -899,24 +889,23 @@ version = "1.17.0+1"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "84eef7acd508ee5b3e956a2ae51b05024181dee0"
 uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
-version = "2.40.2+0"
+version = "2.40.2+2"
 
 [[deps.Libtiff_jll]]
 deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
-git-tree-sha1 = "b404131d06f7886402758c9ce2214b636eb4d54a"
+git-tree-sha1 = "4ab7581296671007fc33f07a721631b8855f4b1d"
 uuid = "89763e89-9b03-5906-acba-b20f662cd828"
-version = "4.7.0+0"
+version = "4.7.1+0"
 
 [[deps.Libuuid_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "edbf5309f9ddf1cab25afc344b1e8150b7c832f9"
 uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
-version = "2.40.2+0"
+version = "2.40.2+2"
 
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-version = "1.11.0"
 
 [[deps.LogExpFunctions]]
 deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
@@ -936,7 +925,6 @@ version = "0.3.29"
 
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
-version = "1.11.0"
 
 [[deps.LoggingExtras]]
 deps = ["Dates", "Logging"]
@@ -946,9 +934,9 @@ version = "1.1.0"
 
 [[deps.Lz4_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "abf88ff67f4fd89839efcae2f4c39cbc4ecd0846"
+git-tree-sha1 = "191686b1ac1ea9c89fc52e996ad15d1d241d1e33"
 uuid = "5ced341a-0733-55b8-9ab6-a4889d929147"
-version = "1.10.0+1"
+version = "1.10.1+0"
 
 [[deps.MPICH_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Hwloc_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"]
@@ -966,18 +954,16 @@ version = "0.1.11"
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"]
 git-tree-sha1 = "70e830dab5d0775183c99fc75e4c24c614ed7142"
 uuid = "f1f71cc9-e9ae-5b93-9b94-4fe0e1ad3748"
-version = "5.5.1+0"
+version = "5.5.1+2"
 
 [[deps.MacroTools]]
-deps = ["Markdown", "Random"]
-git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
+git-tree-sha1 = "72aebe0b5051e5143a079a4685a46da330a40472"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.5.13"
+version = "0.5.15"
 
 [[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
-version = "1.11.0"
 
 [[deps.MbedTLS]]
 deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
@@ -988,7 +974,7 @@ version = "1.1.9"
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
-version = "2.28.6+0"
+version = "2.28.2+1"
 
 [[deps.Measures]]
 git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
@@ -1015,11 +1001,10 @@ version = "1.2.0"
 
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
-version = "1.11.0"
 
 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
-version = "2023.12.12"
+version = "2023.1.10"
 
 [[deps.NDTensors]]
 deps = ["Accessors", "Adapt", "ArrayLayouts", "BlockArrays", "Compat", "Dictionaries", "EllipsisNotation", "FillArrays", "Folds", "Functors", "HalfIntegers", "InlineStrings", "LinearAlgebra", "MacroTools", "PackageExtensionCompat", "Random", "SimpleTraits", "SparseArrays", "SplitApplyCombine", "StaticArrays", "Strided", "StridedViews", "TimerOutputs", "TupleTools", "VectorInterface"]
@@ -1059,9 +1044,9 @@ version = "1.0.2"
 
 [[deps.NetworkLayout]]
 deps = ["GeometryBasics", "LinearAlgebra", "Random", "Requires", "StaticArrays"]
-git-tree-sha1 = "0c51e19351dc1eecc61bc23caaf2262e7ba71973"
+git-tree-sha1 = "90bce32eda5bf1d09dc7282aec2fbae721deace6"
 uuid = "46757867-2c16-5918-afeb-47bfcb05e46a"
-version = "0.4.7"
+version = "0.4.8"
 weakdeps = ["Graphs"]
 
     [deps.NetworkLayout.extensions]
@@ -1072,9 +1057,9 @@ uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
 
 [[deps.OffsetArrays]]
-git-tree-sha1 = "39d000d9c33706b8364817d8894fae1548f40295"
+git-tree-sha1 = "5e1897147d1ff8d98883cda2be2187dcf57d8f0c"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "1.14.2"
+version = "1.15.0"
 weakdeps = ["Adapt"]
 
     [deps.OffsetArrays.extensions]
@@ -1089,7 +1074,7 @@ version = "1.3.5+1"
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
-version = "0.3.27+1"
+version = "0.3.23+4"
 
 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -1112,13 +1097,13 @@ version = "1.4.3"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "3.0.15+1"
+version = "3.0.15+3"
 
 [[deps.OpenSpecFun_jll]]
-deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "1346c9208249809840c91b26703912dff463d335"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
-version = "0.5.5+0"
+version = "0.5.6+0"
 
 [[deps.Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -1144,9 +1129,9 @@ weakdeps = ["Requires", "TOML"]
 
 [[deps.Pango_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801"
+git-tree-sha1 = "ed6834e95bd326c52d5675b4181386dfbe885afb"
 uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
-version = "1.54.1+0"
+version = "1.55.5+0"
 
 [[deps.Parsers]]
 deps = ["Dates", "PrecompileTools", "UUIDs"]
@@ -1166,13 +1151,9 @@ uuid = "30392449-352a-5448-841d-b1acce4e97dc"
 version = "0.43.4+0"
 
 [[deps.Pkg]]
-deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
+deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-version = "1.11.0"
-weakdeps = ["REPL"]
-
-    [deps.Pkg.extensions]
-    REPLExt = "REPL"
+version = "1.10.0"
 
 [[deps.PlotThemes]]
 deps = ["PlotUtils", "Statistics"]
@@ -1239,7 +1220,6 @@ version = "1.4.3"
 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
-version = "1.11.0"
 
 [[deps.PtrArrays]]
 git-tree-sha1 = "77a42d78b6a92df47ab37e177b2deac405e1c88f"
@@ -1283,14 +1263,12 @@ version = "2.11.1"
     Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 
 [[deps.REPL]]
-deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"]
+deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
-version = "1.11.0"
 
 [[deps.Random]]
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-version = "1.11.0"
 
 [[deps.Ratios]]
 deps = ["Requires"]
@@ -1349,7 +1327,6 @@ version = "1.2.1"
 
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
-version = "1.11.0"
 
 [[deps.SerializedElementArrays]]
 deps = ["Serialization"]
@@ -1366,7 +1343,6 @@ version = "1.1.1"
 [[deps.SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
-version = "1.11.0"
 
 [[deps.Showoff]]
 deps = ["Dates", "Grisu"]
@@ -1387,7 +1363,6 @@ version = "0.9.4"
 
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
-version = "1.11.0"
 
 [[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
@@ -1398,7 +1373,7 @@ version = "1.2.1"
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-version = "1.11.0"
+version = "1.10.0"
 
 [[deps.SpecialFunctions]]
 deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
@@ -1447,9 +1422,9 @@ weakdeps = ["OffsetArrays", "StaticArrays"]
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
-git-tree-sha1 = "777657803913ffc7e8cc20f0fd04b634f871af8f"
+git-tree-sha1 = "47091a0340a675c738b1304b58161f3b0839d454"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.9.8"
+version = "1.9.10"
 weakdeps = ["ChainRulesCore", "Statistics"]
 
     [deps.StaticArrays.extensions]
@@ -1462,14 +1437,9 @@ uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 version = "1.4.3"
 
 [[deps.Statistics]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
+deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-version = "1.11.1"
-weakdeps = ["SparseArrays"]
-
-    [deps.Statistics.extensions]
-    SparseArraysExt = ["SparseArrays"]
+version = "1.10.0"
 
 [[deps.StatsAPI]]
 deps = ["LinearAlgebra"]
@@ -1522,14 +1492,10 @@ version = "0.6.21"
     SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
     StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
-[[deps.StyledStrings]]
-uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
-version = "1.11.0"
-
 [[deps.SuiteSparse_jll]]
 deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
-version = "7.7.0+0"
+version = "7.2.1+1"
 
 [[deps.TOML]]
 deps = ["Dates"]
@@ -1577,7 +1543,6 @@ version = "4.1.1"
 [[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-version = "1.11.0"
 
 [[deps.ThreadedScans]]
 deps = ["ArgCheck"]
@@ -1631,11 +1596,9 @@ version = "1.5.1"
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
-version = "1.11.0"
 
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
-version = "1.11.0"
 
 [[deps.UnicodeFun]]
 deps = ["REPL"]
@@ -1645,9 +1608,9 @@ version = "0.4.1"
 
 [[deps.Unitful]]
 deps = ["Dates", "LinearAlgebra", "Random"]
-git-tree-sha1 = "01915bfcd62be15329c9a07235447a89d588327c"
+git-tree-sha1 = "c0667a8e676c53d390a09dc6870b3d8d6650e2bf"
 uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
-version = "1.21.1"
+version = "1.22.0"
 weakdeps = ["ConstructionBase", "InverseFunctions"]
 
     [deps.Unitful.extensions]
@@ -1679,15 +1642,15 @@ version = "1.3.243+0"
 
 [[deps.Wayland_jll]]
 deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
-git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
+git-tree-sha1 = "85c7811eddec9e7f22615371c3cc81a504c508ee"
 uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
-version = "1.21.0+1"
+version = "1.21.0+2"
 
 [[deps.Wayland_protocols_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
+git-tree-sha1 = "5db3e9d307d32baba7067b13fc7b5aa6edd4a19a"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.31.0+0"
+version = "1.36.0+0"
 
 [[deps.WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
@@ -1709,9 +1672,9 @@ version = "1.1.42+0"
 
 [[deps.XZ_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "15e637a697345f6743674f1322beefbc5dcd5cfc"
+git-tree-sha1 = "beef98d5aad604d9e7d60b2ece5181f7888e2fd6"
 uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
-version = "5.6.3+0"
+version = "5.6.4+0"
 
 [[deps.Xorg_libICE_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
@@ -1729,43 +1692,43 @@ version = "1.2.4+0"
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
 git-tree-sha1 = "9dafcee1d24c4f024e7edc92603cedba72118283"
 uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
-version = "1.8.6+1"
+version = "1.8.6+3"
 
 [[deps.Xorg_libXau_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "2b0e27d52ec9d8d483e2ca0b72b3cb1a8df5c27a"
 uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
-version = "1.0.11+1"
+version = "1.0.11+3"
 
 [[deps.Xorg_libXcursor_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
-git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "807c226eaf3651e7b2c468f687ac788291f9a89b"
 uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
-version = "1.2.0+4"
+version = "1.2.3+0"
 
 [[deps.Xorg_libXdmcp_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "02054ee01980c90297412e4c809c8694d7323af3"
 uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
-version = "1.1.4+1"
+version = "1.1.4+3"
 
 [[deps.Xorg_libXext_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
 git-tree-sha1 = "d7155fea91a4123ef59f42c4afb5ab3b4ca95058"
 uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
-version = "1.3.6+1"
+version = "1.3.6+3"
 
 [[deps.Xorg_libXfixes_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
-git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "6fcc21d5aea1a0b7cce6cab3e62246abd1949b86"
 uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
-version = "5.0.3+4"
+version = "6.0.0+0"
 
 [[deps.Xorg_libXi_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
-git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "984b313b049c89739075b8e2a94407076de17449"
 uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
-version = "1.7.10+4"
+version = "1.8.2+0"
 
 [[deps.Xorg_libXinerama_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
@@ -1789,13 +1752,13 @@ version = "0.9.11+1"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "fee57a273563e273f0f53275101cd41a8153517a"
 uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
-version = "0.1.1+1"
+version = "0.1.1+3"
 
 [[deps.Xorg_libxcb_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
 git-tree-sha1 = "1a74296303b6524a0472a8cb12d3d87a78eb3612"
 uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
-version = "1.17.0+1"
+version = "1.17.0+3"
 
 [[deps.Xorg_libxkbfile_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
@@ -1855,7 +1818,7 @@ version = "2.39.0+0"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "b9ead2d2bdb27330545eb14234a2e300da61232e"
 uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
-version = "1.5.0+1"
+version = "1.5.0+3"
 
 [[deps.Zeros]]
 deps = ["Test"]
@@ -1870,9 +1833,9 @@ version = "1.2.13+1"
 
 [[deps.Zstd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b"
+git-tree-sha1 = "622cf78670d067c738667aaa96c553430b65e269"
 uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
-version = "1.5.6+1"
+version = "1.5.7+0"
 
 [[deps.eudev_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
@@ -1896,13 +1859,13 @@ version = "3.1.1+1"
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "46bf7be2917b59b761247be3f317ddf75e50e997"
 uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0"
-version = "1.1.2+0"
+version = "1.1.2+2"
 
 [[deps.libaom_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
-git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
+git-tree-sha1 = "522c1df09d05a71785765d19c9524661234738e9"
 uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
-version = "3.9.0+0"
+version = "3.11.0+0"
 
 [[deps.libass_jll]]
 deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
@@ -1941,9 +1904,9 @@ version = "1.18.0+0"
 
 [[deps.libpng_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
-git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280"
+git-tree-sha1 = "b7bfd3ab9d2c58c3829684142f5804e4c6499abc"
 uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
-version = "1.6.44+0"
+version = "1.6.45+0"
 
 [[deps.libvorbis_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
@@ -1960,7 +1923,7 @@ version = "1.1.6+0"
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
-version = "1.59.0+0"
+version = "1.52.0+1"
 
 [[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -1981,6 +1944,6 @@ version = "3.5.0+0"
 
 [[deps.xkbcommon_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
-git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+git-tree-sha1 = "63406453ed9b33a0df95d570816d5366c92b7809"
 uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
-version = "1.4.1+1"
+version = "1.4.1+2"
diff --git a/docs/Project.toml b/docs/Project.toml
index 43ecaae..8e3c54e 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -2,4 +2,4 @@
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 
 [compat]
-Documenter = "1.8"
+Documenter = "1.8"
\ No newline at end of file
diff --git a/docs/src/examples/puredephasing.md b/docs/src/examples/puredephasing.md
index 0f45c40..e7c3a81 100644
--- a/docs/src/examples/puredephasing.md
+++ b/docs/src/examples/puredephasing.md
@@ -114,7 +114,7 @@ This initial state is a product state between the system and the chain. It is co
 # MPO and initial state MPS
 #---------------------------
 
-H = puredephasingmpo(ΔE, d, N, cpars)
+H = puredephasingmpo(ω0, d, N, cpars)
 
 # Initial electronic system in a superposition of 1 and 2
 ψ = zeros(2)
@@ -142,7 +142,7 @@ A, dat = runsim(dt, tfinal, A, H, prec=1E-4;
                 method = method,
                 obs = [ob1],
                 convobs = [ob1],
-                params = @LogParams(ΔE, N, d, α, s),
+                params = @LogParams(ω0, N, d, α, s),
                 convparams = D,
                 reduceddensity=true,
                 verbose = false,
diff --git a/docs/src/examples/timedep.md b/docs/src/examples/timedep.md
index df761a9..6ef5c3b 100644
--- a/docs/src/examples/timedep.md
+++ b/docs/src/examples/timedep.md
@@ -164,7 +164,7 @@ ob3 = TwoSiteObservable("SXdisp", sx, disp(d), [1], collect(2:N+1))
 A, dat = runsim(dt, tfinal, A, H;
                 name = "Driving field on ohmic spin boson model",
                 method = method,
-                obs = [ob1],
+                obs = [ob1, ob2, ob3],
                 convobs = [ob1],
                 params = @LogParams(N, d, α, Δ, ω0, s),
                 convparams = D,
@@ -176,7 +176,7 @@ A, dat = runsim(dt, tfinal, A, H;
                 plot = true,
                 );
 ```
-Eventually, the stored observables can be represented. For more information about the chain observables, see [Inspecting the bath by undoing the chain mapping] 
+Eventually, the stored observables can be represented. For more information about the chain observables, see [Inspecting the bath by undoing the chain mapping](@ref) 
 ```julia
 
 #----------
diff --git a/docs/src/methods.md b/docs/src/methods.md
index 98ed7ee..370352b 100644
--- a/docs/src/methods.md
+++ b/docs/src/methods.md
@@ -44,5 +44,5 @@ Pages = ["MPSDynamics.jl", "chain2TDVP.jl", "chainA1TDVP.jl","chainDMRG.jl","cha
 ## Advanced
 ```@autodocs
 Modules = [MPSDynamics]
-Pages = ["flattendict.jl", "logging.jl", "logiter.jl","machines.jl"]
+Pages = ["flattendict.jl", "logging.jl", "logiter.jl","machines.jl","utilities.jl"]
 ```
diff --git a/src/MPSDynamics.jl b/src/MPSDynamics.jl
index 65e9e95..03aeca8 100644
--- a/src/MPSDynamics.jl
+++ b/src/MPSDynamics.jl
@@ -28,6 +28,7 @@ include("run_DTDVP.jl")
 include("chainA1TDVP.jl")
 include("switchmpo.jl")
 include("finitetemperature.jl")
+include("utilities.jl")
 
 """
     runsim(dt, tmax, A, H; 
@@ -87,12 +88,16 @@ function runsim(dt, tmax, A, H;
         convparams = typeof(convparams) <: Vector ? only(convparams) : convparams
     end
 
-    if save || plot
+    if save || plot || (:onthefly in keys(kwargs) && !isempty(kwargs[:onthefly][:save_obs]) && kwargs[:onthefly][:savedir] == "auto")
         if savedir[end] != '/'
             savedir = string(savedir,"/")
         end
         isdir(savedir) || mkdir(savedir)
         open_log(dt, tmax, convparams, method, machine, savedir, unid, name, params, obs, convobs, convcheck, kwargs...)
+        if :onthefly in keys(kwargs)
+            mkdir(string(savedir, unid, "/tmp/"))
+            kwargs[:onthefly][:savedir] = string(savedir, unid, "/tmp/")
+        end
     end
 
     paramdict = Dict([[(par[1], par[2]) for par in params]...,
@@ -155,7 +160,7 @@ export chaincoeffs_ohmic, spinbosonmpo, methylbluempo, methylbluempo_correlated,
 
 export productstatemps, physdims, randmps, bonddims, elementmps
 
-export measure, measurempo, OneSiteObservable, TwoSiteObservable, FockError, errorbar
+export measure, measurempo, OneSiteObservable, TwoSiteObservable, RhoReduced, FockError, errorbar
 
 export runsim, run_all
 
@@ -175,5 +180,7 @@ export rhoreduced_2sites, rhoreduced_1site, protontransfermpo
 
 export chaincoeffs_finiteT, chaincoeffs_fermionic, fermionicspectraldensity_finiteT, chaincoeffs_finiteT_discrete
 
+export onthefly, mergetmp
+
 end
 
diff --git a/src/measure.jl b/src/measure.jl
index 3122f7b..cc7787a 100644
--- a/src/measure.jl
+++ b/src/measure.jl
@@ -35,6 +35,17 @@ struct TwoSiteObservable <: Observable
     allsites::Bool
 end
 
+"""
+    RhoReduced(name,sites)
+
+Computes the reduced density matrix on the sites `sites` which can be either a single site or a tuple of two sites. Used to define
+reduced density matrices that are obs and convobs parameters for the `runsim` function.
+"""
+struct RhoReduced <: Observable
+    name::String
+    sites::Union{Int, Tuple{Int, Int}}
+end
+
 struct CdagCup <: Observable
     name::String
     sites::Tuple{Int,Int}
@@ -183,6 +194,7 @@ measure(A, O::TwoSiteObservable, ::Nothing) =
     measure2siteoperator(A, O.op1, O.op2, O.sites1, O.sites2)
 measure(A, O::TwoSiteObservable, ρ::Vector) =
     measure2siteoperator(A, O.op1, O.op2, O.sites1, O.sites2, ρ)
+measure(A, O::RhoReduced; kwargs...) = O.sites isa Int ? rhoreduced_1site(A, O.sites) : rhoreduced_2sites(A, O.sites)
 
 """
     measure1siteoperator(A::Vector, O, sites::Vector{Int})
diff --git a/src/run_1TDVP.jl b/src/run_1TDVP.jl
index 50daa57..c743041 100644
--- a/src/run_1TDVP.jl
+++ b/src/run_1TDVP.jl
@@ -1,4 +1,4 @@
-function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=false, timedep=false, kwargs...)
+function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=false, timedep=false, progressbar=true, onthefly=Dict(), kwargs...)
     A0=deepcopy(A)
     H0=deepcopy(H)
     data = Dict{String,Any}()
@@ -19,12 +19,19 @@ function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=fal
     end
 
     timed && (ttdvp = Vector{Float64}(undef, numsteps))
+    onthefly = copy(onthefly)
+    ontheflyplotbool = !isempty(onthefly) && !isnothing(onthefly[:plot_obs])
+    ontheflysavebool =  !isempty(onthefly) && !isempty(onthefly[:save_obs])
+    ontheflysavebool && (onthefly[:save_obs] = intersect(onthefly[:save_obs], [ob.name for ob in obs]))
 
     F=nothing
     mpsembed!(A0, Dmax)
-    for tstep=1:numsteps
-        @printf("%i/%i, t = %.3f ", tstep, numsteps, times[tstep])
-        println()
+    iter = progressbar ? ProgressBar(numsteps; ETA=true) : 1:numsteps
+    for tstep in iter
+        if !progressbar
+            @printf("%i/%i, t = %.3f ", tstep, numsteps, times[tstep])
+            println()
+        end
         if timedep
 	   Ndrive = kwargs[:Ndrive]
 	   Htime = kwargs[:Htime]
@@ -55,6 +62,8 @@ function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=fal
             exprho = rhoreduced_1site(A0,Nrho)
             data["Reduced ρ"] = cat(data["Reduced ρ"], exprho; dims=ndims(exprho)+1)
         end
+        ontheflyplotbool && tstep%onthefly[:step] == 0 && ontheflyplot(onthefly, tstep, times, data)
+        ontheflysavebool && tstep%onthefly[:step] == 0 && ontheflysave(onthefly, tstep, times, data)
     end
     timed && push!(data, "deltat"=>ttdvp)
     push!(data, "times" => times)
diff --git a/src/run_2TDVP.jl b/src/run_2TDVP.jl
index d7e22fe..aa06b59 100644
--- a/src/run_2TDVP.jl
+++ b/src/run_2TDVP.jl
@@ -1,4 +1,4 @@
-function run_2TDVP(dt, tmax, A, H, truncerr; obs=[], Dlim=50, savebonddims=false, timed=false, reduceddensity=false, timedep=false, kwargs...)
+function run_2TDVP(dt, tmax, A, H, truncerr; obs=[], Dlim=50, savebonddims=false, timed=false, reduceddensity=false, timedep=false, progressbar=true, onthefly=Dict(), kwargs...)
     A0=deepcopy(A)
     H0=deepcopy(H)
     data = Dict{String,Any}()
@@ -22,12 +22,19 @@ function run_2TDVP(dt, tmax, A, H, truncerr; obs=[], Dlim=50, savebonddims=false
     savebonddims && push!(data, "bonddims" => reshape([bonds...], length(bonds), 1))
 
     timed && (ttdvp = Vector{Float64}(undef, numsteps))
+    onthefly = copy(onthefly)
+    ontheflyplotbool = !isempty(onthefly) && !isnothing(onthefly[:plot_obs])
+    ontheflysavebool =  !isempty(onthefly) && !isempty(onthefly[:save_obs])
+    ontheflysavebool && (onthefly[:save_obs] = intersect(onthefly[:save_obs], [ob.name for ob in obs]))
 
     F=nothing
-    for tstep=1:numsteps
-        maxbond = max(bonds...)
-        @printf("%i/%i, t = %.3f, Dmax = %i ", tstep, numsteps, times[tstep], maxbond)
-        println()
+    iter = progressbar ? ProgressBar(numsteps; ETA=false) : 1:numsteps
+    for tstep in iter
+        if !progressbar
+            maxbond = max(bonds...)
+            @printf("%i/%i, t = %.3f, Dmax = %i ", tstep, numsteps, times[tstep], maxbond)
+            println()
+        end
         if timedep
            Ndrive = kwargs[:Ndrive]
            Htime = kwargs[:Htime]
@@ -52,6 +59,8 @@ function run_2TDVP(dt, tmax, A, H, truncerr; obs=[], Dlim=50, savebonddims=false
             A0, F = tdvp2sweep!(dt, A0, H0, F; truncerr=truncerr, truncdim=Dlim, kwargs...)
         end
         bonds = bonddims(A0)
+        progressbar && (maxbond = max(bonds...))
+        progressbar && (iter.Dmax = maxbond)
         exp = measure(A0, obs; t=times[tstep])
         for (i, ob) in enumerate(obs)
             data[ob.name] = cat(data[ob.name], exp[i], dims=ndims(exp[i])+1)
@@ -63,6 +72,8 @@ function run_2TDVP(dt, tmax, A, H, truncerr; obs=[], Dlim=50, savebonddims=false
         if savebonddims
             data["bonddims"] = cat(data["bonddims"], [bonds...], dims=2)
         end
+        ontheflyplotbool && tstep%onthefly[:step] == 0 && ontheflyplot(onthefly, tstep, times, data)
+        ontheflysavebool && tstep%onthefly[:step] == 0 && ontheflysave(onthefly, tstep, times, data)
     end
     timed && push!(data, "deltat"=>ttdvp)
     push!(data, "times" => times)
diff --git a/src/run_DTDVP.jl b/src/run_DTDVP.jl
index 7689a66..4cf97a9 100644
--- a/src/run_DTDVP.jl
+++ b/src/run_DTDVP.jl
@@ -1,4 +1,4 @@
-function run_DTDVP(dt, tmax, A, H, prec; obs=[], effects=false, error=false, timed=false, savebonddims=false, Dplusmax=nothing, Dlim=50, reduceddensity=false, timedep=false, kwargs...)
+function run_DTDVP(dt, tmax, A, H, prec; obs=[], effects=false, error=false, timed=false, savebonddims=false, Dplusmax=nothing, Dlim=50, reduceddensity=false, timedep=false, progressbar=true, onthefly=Dict(), kwargs...)
     A0=deepcopy(A)
     H0=deepcopy(H)
     data = Dict{String,Any}()
@@ -25,12 +25,19 @@ function run_DTDVP(dt, tmax, A, H, prec; obs=[], effects=false, error=false, tim
     timed && (ttdvp = Vector{Float64}(undef, numsteps))
     timed && (tproj = Vector{Float64}(undef, numsteps))
     effects && (efft = Vector{Any}(undef, numsteps))
+    onthefly = copy(onthefly)
+    ontheflyplotbool = !isempty(onthefly) && !isnothing(onthefly[:plot_obs])
+    ontheflysavebool =  !isempty(onthefly) && !isempty(onthefly[:save_obs])
+    ontheflysavebool && (onthefly[:save_obs] = intersect(onthefly[:save_obs], [ob.name for ob in obs]))
 
     F=nothing
     Afull=nothing
-    for tstep=1:numsteps
-        maxbond = max(bonds...)
-        @printf("%i/%i, t = %.3f, Dmax = %i \n", tstep, numsteps, times[tstep], maxbond)
+    iter = progressbar ? ProgressBar(numsteps; ETA=false) : 1:numsteps
+    for tstep in iter
+        if !progressbar
+            maxbond = max(bonds...)
+            @printf("%i/%i, t = %.3f, Dmax = %i \n", tstep, numsteps, times[tstep], maxbond)
+        end
         if timedep
            Ndrive = kwargs[:Ndrive]
            Htime = kwargs[:Htime]
@@ -58,6 +65,9 @@ function run_DTDVP(dt, tmax, A, H, prec; obs=[], effects=false, error=false, tim
         
         exp = info["obs"]
         bonds = info["dims"]
+        progressbar && (maxbond = max(bonds...))
+        progressbar && (iter.Dmax = maxbond)
+
         effects && (efft[tstep] = reduce(hcat, info["effect"]))
         error && (errs[tstep] = info["err"])
         timed && (ttdvp[tstep] = info["t2"] + info["t3"])
@@ -71,6 +81,8 @@ function run_DTDVP(dt, tmax, A, H, prec; obs=[], effects=false, error=false, tim
                 exprho = rhoreduced_1site(A0,Nrho)
             	data["Reduced ρ"] = cat(data["Reduced ρ"], exprho; dims=ndims(exprho)+1)
             end
+            ontheflyplotbool && (tstep-1)%onthefly[:step] == 0 && ontheflyplot(onthefly, tstep-1, times, data)
+            ontheflysavebool && (tstep-1)%onthefly[:step] == 0 && ontheflysave(onthefly, tstep-1, times, data)
         end
         if savebonddims
             data["bonddims"] = cat(data["bonddims"], bonds, dims=2)
diff --git a/src/utilities.jl b/src/utilities.jl
new file mode 100644
index 0000000..012970e
--- /dev/null
+++ b/src/utilities.jl
@@ -0,0 +1,130 @@
+mutable struct ProgressBar
+    numsteps::Int
+    ETA::Bool
+    times::Vector{<:Float64}
+    Dmax::Int
+    length::UInt
+end
+
+"""
+    ProgressBar(numsteps::Int; ETA=false, last=10)
+
+An iterable returning values from 1 to `numsteps`. Displays a progress bar for the for loop where it has been called.
+If ETA is true then displays an estimation of the remaining time calculated based on the time spent computing the last `last` values.
+The progress bar can be activated or deactivated by setting the `progressbar` keyword argument in `runsim` to true or false."""
+ProgressBar(numsteps::Int; ETA=false, last=10) = ProgressBar(numsteps, ETA, fill(0., (ETA ? last : 1)+1), 0, displaysize(stdout)[2] > 54 ? min(displaysize(stdout)[2]-54, 50) : error("Error : Terminal window too narrow"))
+
+function Base.iterate(bar::ProgressBar, state=1)
+    Ntimes = length(bar.times)-1
+    if state > bar.numsteps
+        println()
+        return nothing
+    elseif state == 1
+        printstyled("\nCompiling..."; color=:red, bold=true)
+        bar.times = fill(time(), Ntimes+1)
+    else
+        tnow = time()
+        dtelapsed = tnow - bar.times[1]
+        dtETA = (tnow - bar.times[2+state%Ntimes])*(bar.numsteps - state)/min(state-1, Ntimes)
+        dtiter = tnow - bar.times[2+(state-1)%Ntimes]
+        bar.times[2+state%Ntimes] = tnow
+        elapsedstr = Dates.format(Time(0)+Second(floor(Int, dtelapsed)), dtelapsed>3600 ? "HH:MM:SS" : "MM:SS")
+        ETAstr = Dates.format(Time(0)+Second(floor(Int, dtETA)), dtETA>3600 ? "HH:MM:SS" : "MM:SS")
+        iterstr = Dates.format(Time(0)+Millisecond(floor(Int, 1000*dtiter)), dtiter>60 ? "MM:SS.sss" : "SS.sss")
+        print("\r")
+        printstyled("$(round(100*state/bar.numsteps, digits=1))% "; color = :green, bold=true)
+        print("┣"*"#"^(round(Int, state/bar.numsteps*bar.length))*" "^(bar.length-round(Int, state/bar.numsteps*bar.length))*"┫")
+        printstyled(" $state/$(bar.numsteps) [$(elapsedstr)s"*(bar.ETA ? "; ETA:$(ETAstr)s" : "")*"; $(iterstr)s/it"*(bar.Dmax > 0 ? "; Dmax=$(bar.Dmax)" : "")*"]"; color = :green, bold=true)
+    end
+    return (state, state+1)
+end
+
+"""
+    onthefly(;plot_obs=nothing::Union{<:Observable, Nothing}, save_obs=Vector{Observable}(undef, 0)::Union{<:Observable, Vector{<:Observable}}, savedir="auto", step=10::Int, func=identity<:Function, compare=nothing::Union{Tuple{Vector{Float64}, Vector{Float64}}, Nothing}, clear=identity<:Function)
+
+Helper function returning a dictionnary containing the necessary arguments for on the fly plotting or saving in the `runsim` function.
+
+# Arguments
+
+* `plot_obs` : Observable to plot
+* `save_obs` : List of Observable(s) to save
+* `savedir` : Used to specify the path where temporary files are stored, default is `"auto"` which saves in a "tmp" folder in the run folder (generally located at "~/MPSDynamics/<unid>/tmp/"). 
+* `step` : Number of time steps every which the function plots or saves the data
+* `func` : Function to apply to the result of measurement of plot_obs (for example `real` or `abs` to make a complex result possible to plot)
+* `compare` : Tuple `(times, data)` of previous results to compare against the plot_obs results,
+* `clear` : Function used to clear the output before each attempt to plot, helpful for working in Jupyter notebooks where clear=IJulia.clear_output allows to reduce the size of the cell output
+
+# Examples
+
+For example in the [Spin-Boson model example](@ref "The Spin Boson Model"), adding the following argument to the `runsim` function allows to save
+the "sz" observable `ob1` in the directory "~/MPSDynamics/<unid>/tmp/" and plot its real part during the simulation:
+```julia
+runsim(..., onthefly=onthefly(plot_obs=ob1, save_obs=[ob1], savedir="auto", step=10, func=real))
+```
+To merge the temporary files in one usable file, one can then use [`MPSDynamics.mergetmp`](@ref).
+"""
+function onthefly(;plot_obs=nothing::Union{<:Observable, Nothing}, save_obs=Vector{Observable}(undef, 0)::Union{<:Observable, Vector{<:Observable}}, savedir="auto", step=10::Int, func=identity::Function, compare=nothing::Union{Tuple{Vector{Float64}, Vector{Float64}}, Nothing}, clear=nothing)
+    if isnothing(plot_obs) && isempty(save_obs)
+        error("Must provide an observable to plot/save")
+    end
+    # !isempty(save_obs) && (isdir(savedir) || mkdir(savedir))
+    plt = isnothing(plot_obs) ? nothing : plot(title="Intermediate Results", xlabel="t", ylabel=plot_obs.name)
+    !isnothing(compare) && plot!(compare)
+    println("On the fly mode activated")
+    return Dict(:plot_obs => isnothing(plot_obs) ? nothing : plot_obs.name, :save_obs => [ob.name for ob in save_obs], :savedir => savedir, :step => step, :func => func, :clear => clear, :compare => compare, :plot => plt)
+end
+
+"""
+    ontheflyplot(onthefly, tstep, times, data)
+
+Plots data according to the arguments of the `onthefly` dictionnary."""
+function ontheflyplot(onthefly, tstep, times, data)
+    tstep < onthefly[:step]+2 && plot!(onthefly[:plot], [], [])
+    N = ndims(data[onthefly[:plot_obs]])
+    N == 1 ? slicefunc(arr, N, i) = arr[i] : slicefunc = selectdim
+    append!(onthefly[:plot].series_list[end], times[tstep-onthefly[:step]+1:tstep+1], map(onthefly[:func], (slicefunc(data[onthefly[:plot_obs]], N, i) for i in (tstep-onthefly[:step]+1):(tstep+1))))
+    !isnothing(onthefly[:clear]) && onthefly[:clear](true)
+    sleep(0.05);display(onthefly[:plot])
+end
+
+"""
+    ontheflysave(onthefly, tstep, times, data)
+
+Saves data according to the arguments of the `onthefly` dictionnary."""
+function ontheflysave(onthefly, tstep, times, data)
+    jldopen(onthefly[:savedir]*"tmp$(tstep÷onthefly[:step]).jld", "w") do file
+        write(file, "times", times[tstep-onthefly[:step]+1:tstep+1])
+        for name in onthefly[:save_obs]
+            write(file, name, data[name][tstep-onthefly[:step]+1:tstep+1])
+        end
+    end
+end
+
+"""
+    mergetmp(tmpdir; fields=[], overwrite=true)
+
+Merges the temporary files created by the `ontheflysave` function at the directory `tmpdir` and returns a dictionnary containing the resulting data.
+By default all fields are present but one can select the fields of interest with a list of names in `fields`."""
+function mergetmp(tmpdir; fields=[], overwrite=true)
+    tmpdir[end] != '/' && (tmpdir *= '/')
+    !isdir(tmpdir) && error("Choose a valid directory")
+    files = [walkdir(tmpdir)...][1][3]
+    files = filter(x->!isnothing(match(r"tmp(\d+).jld", x)), files)
+    files = sort(files, by=(x -> parse(Int, match(r"(\d+)", x).captures[1])))
+    isempty(fields) && (fields = keys(JLD.load(tmpdir*files[1])))
+    merged_data = Dict(ob => [] for ob in fields)
+    i = 1
+    for file in files
+        for ob in fields
+            append!(merged_data[ob], JLD.load(tmpdir*file, ob))
+        end
+        i += 1
+    end
+    if overwrite
+        for file in files
+            rm(tmpdir*file)
+        end
+        JLD.save(tmpdir*files[end], Iterators.flatten(merged_data)...)
+    end
+    return merged_data
+end
\ No newline at end of file