[WIP] Add two-site DMRG for tree tensor networks

[mtfishman]

Summary

Adds dmrg, a two-site DMRG ground-state solver for tree tensor networks, built on the same layered AlgorithmsInterface structure as beliefpropagation and apply_operators. It works on any tree, gauges the state with isometric (QR) orthogonalization, and holds the projected-Hamiltonian environments in a MessageCache.

The operator is passed as a TensorNetworkOperator, a tensor network together with the map between its bra-side and ket-side physical names (the tensor-network analogue of a NamedDimsArrays operator). A QuadraticFormNetwork wraps the lazy ⟨ψ|H|ψ⟩ and derives the bra layer from the ket, so it tracks updates to the state. On a tree the environments are exact: each per-edge message is the contraction of the ⟨ψ|H|ψ⟩ subtree on one side of the cut, carried as a NamedDimsArrays operator whose codomain and domain record the bra-to-ket link correspondence, so the bra link names generated internally are queryable from the returned environment.

The environment is built once per solve and kept current incrementally as the orthogonality center walks to each region, so a sweep stays linear in the number of sites. Truncation can vary across sweeps through a trunc function of the sweep index, and stopping_criterion takes (; maxsweeps, tol) (a sweep cap and an energy-convergence tolerance) or an explicit criterion.

The effective Hamiltonian is currently materialized into a single operator tensor rather than applied matrix-free. A matrix-free version is a planned follow-up.

TODO

• Move the VectorInterface methods on AbstractNamedDimsArray (needed by KrylovKit.eigsolve) into NamedDimsArrays, then drop the broken marker on the Aqua piracy check.

[codecov]

Codecov Report

❌ Patch coverage is 83.71041% with 36 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.97%. Comparing base (e312bd5) to head (c0217eb).

Files with missing lines	Patch %	Lines
src/dmrg.jl	87.07%	19 Missing ⚠️
src/orthogonalize.jl	69.56%	7 Missing ⚠️
src/tensornetworkoperator.jl	54.54%	5 Missing ⚠️
src/quadraticformnetwork.jl	90.62%	3 Missing ⚠️
src/nameddimsarrays_extensions.jl	75.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #122      +/-   ##
==========================================
+ Coverage   74.79%   74.97%   +0.18%     
==========================================
  Files          24       26       +2     
  Lines        1079     1247     +168     
==========================================
+ Hits          807      935     +128     
- Misses        272      312      +40     

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