Add two-site DMRG for tree tensor networks

Adds `dmrg`, a two-site DMRG ground-state solver for trees: the operator is a
`TensorNetworkOperator`, the exact projected-Hamiltonian environments live in a
`MessageCache` of `NamedDimsArrays` operators, and the driver follows the layered
`AlgorithmsInterface` structure used by `beliefpropagation` and `apply_operators`.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Author: mtfishman

Project.toml

@@ -1,6 +1,6 @@
 name = "ITensorNetworksNext"
 uuid = "302f2e75-49f0-4526-aef7-d8ba550cb06c"
-version = "0.4.4"
+version = "0.4.5"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 
 [workspace]
@@ -17,6 +17,7 @@ DiagonalArrays = "74fd4be6-21e2-4f6f-823a-4360d37c7a77"
 Dictionaries = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
 FunctionImplementations = "7c7cc465-9c6a-495f-bdd1-f42428e86d0c"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
@@ -28,6 +29,7 @@ SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
 TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 TermInterface = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
 TypeParameterAccessors = "7e5a90cf-f82e-492e-a09b-e3e26432c138"
+VectorInterface = "409d34a3-91d5-4945-b6ec-7529ddf182d8"
 WrappedUnions = "325db55a-9c6c-5b90-b1a2-ec87e7a38c44"
 
 [weakdeps]
@@ -47,6 +49,7 @@ DiagonalArrays = "0.3.31"
 Dictionaries = "0.4.5"
 FunctionImplementations = "0.4.1"
 Graphs = "1.13.1"
+KrylovKit = "0.10"
 LinearAlgebra = "1.10"
 MacroTools = "0.5.16"
 MatrixAlgebraKit = "0.6"
@@ -59,5 +62,6 @@ TensorAlgebra = "0.9.5"
 TensorOperations = "5.3.1"
 TermInterface = "2"
 TypeParameterAccessors = "0.4.4"
+VectorInterface = "0.5"
 WrappedUnions = "0.3"
 julia = "1.10"

src/ITensorNetworksNext.jl

@@ -3,7 +3,7 @@ module ITensorNetworksNext
 if VERSION >= v"1.11.0-DEV.469"
     eval(
         Meta.parse(
-            "public apply_operator, apply_operators, beliefpropagation_normnetwork, identity_norm_message_env, normnetwork, norm_message_env, ones_norm_message_env, rand_norm_message_env, randn_norm_message_env, similar_norm_message_env"
+            "public apply_operator, apply_operators, beliefpropagation_normnetwork, dmrg, identity_norm_message_env, normnetwork, norm_message_env, ones_norm_message_env, rand_norm_message_env, randn_norm_message_env, similar_norm_message_env, StopWhenEnergyConverged, TensorNetworkOperator"
         )
     )
 end
@@ -22,4 +22,6 @@ include("beliefpropagation/normnetwork.jl")
 
 include("apply/apply_operators.jl")
 
+include("dmrg.jl")
+
 end