Tensor-Network Documentation

This directory combines current tensor-network design constraints, the pure-Uni20 finite BlockTensor DMRG path, and retained findings from the historical tensorcontraction-integration branch. Host and single-device resident-CUDA U(1) sweeps now use the current Tensor, symmetry, dispatch, Async, and CUDA architecture. The reference branch remains useful for MPI and later distributed-execution targets rather than defining current capability.

Current Main-Branch Foundations

• Symmetry documents the quantum-number and block-space foundations that are present on main.
• Tensor Operations and Tensor-Network Linear Algebra API Survey document the dense kernels used below BlockTensor operations.
• First Pure-Uni20 Two-Site DMRG Slice documents the implemented U(1) local and MPO/environment effective- Hamiltonian, Lanczos, and staged block-SVD integration checkpoints.
• MPO Environment Updates specifies identity boundaries and the implemented left/right symmetry-preserving updates.
• Finite Chains And Environment Caches specifies validated MPS/MPO ownership, revision-tracked replacement, lazy directional cache construction, and exact invalidation ranges.
• Directional Two-Site MPS Splitting specifies staged state selection, sweep-direction singular-value absorption, canonical site materialization, and finite-chain replacement.
• Directional Two-Site DMRG Sweeps specifies local ground-state solving, mutation boundaries, traversal order, and incremental environment refresh.
• DMRG Performance Baselines records the first CPU and resident-CUDA scaling measurements, external orientation points, benchmarking rules, block scheduling, provider-resource conclusions, and implemented per-sector SVD parallelism.
• Spin-Half Model Builders specifies the implemented U(1) local space, normalized Néel product MPS, and reduced-boundary open Heisenberg MPO.

TensorContraction Integration Reference

• Sparse Matrices, Local Operators, and Finite MPS and DMRG document the functional branch implementation. They are capability and migration references, not a source inventory for main. The model guide above now distinguishes its implemented spin-half surface from later integration-branch model targets.
• TensorContraction Integration Findings records measured conclusions from the working CUDA/MPI integration.
• R/A/B/C Contraction Scheduling develops the intended pure-Uni20 replacement for the effective-Hamiltonian scheduling and cost model.
• R/A/B/C Lanczos Fixtures records the capture and replay workflow used to preserve numerical and performance evidence.

The MPI R/A/B/C fixture executors remain runnable only on the integration branch. Pure Uni20 now implements validated finite MPS/MPO owners, directional environment caches, a sparse R/A/B/C compiler and dispatched host/CUDA executor, matrix-free local Krylov solves, selected block-SVD pair replacement, directional two-site traversal, alternating terminal-energy convergence, and resident single-device CUDA storage throughout the working state. The remaining program includes post-truncation measurements, general initial-state canonicalization, broader models and symmetries, multi-GPU placement, MPI distribution, and continued performance work without retaining the external TensorContraction code lineage. The integration branch's measured behavior continues to supply design constraints and regression targets.

Relevant current source foundations are the dense Tensor layer, symmetry metadata, and low-level tensor kernels. Current physical-model construction lives in the model layer.