Tenax

JAX-based tensor network library with symmetry-aware block-sparse tensors.

Tenax provides label-based tensor contraction (Cytnx-style), abelian symmetry support (U(1), Z_n), and production-ready implementations of DMRG, TRG, HOTRG, and iPEPS algorithms.

Key Features

• Label-based contraction – shared labels between tensors are automatically contracted; no manual einsum subscripts needed.

• Symmetry-aware tensors – SymmetricTensor stores only symmetry-allowed charge sectors, reducing memory and FLOPs.

• JAX integration – all tensor types are registered as JAX pytrees for seamless jit, grad, and vmap.

• Optimised contraction paths – opt_einsum finds the best contraction order before JAX executes.

• Batteries-included algorithms – DMRG, TRG, HOTRG, iPEPS with simple configuration dataclasses.

Getting Started

User Guide

• Installation
  • Prerequisites
  • Install with pip
  • Install with uv (recommended for development)
  • Hardware acceleration
  • Building the documentation
  • Float64 precision
  • Verifying the installation
• Quickstart
  • Example 1 – Tensor creation and contraction
  • Example 2 – DMRG ground state of the Heisenberg chain
  • Example 3 – 2D Ising free energy with TRG
  • Next steps
• Core Concepts
  • Symmetries
  • Indices
  • Tensors
• Contraction, SVD, and QR
  • Label-based contraction
  • Truncated SVD
  • QR decomposition
  • Lower-level API
• Tensor Networks
  • Creating a network
  • Querying the network
  • Contraction
  • Modifying the network
  • Building an MPS
  • Building a PEPS
• Gotchas
  • Float64 precision and JAX_ENABLE_X64
  • MPO index convention
  • NumPy >= 2.0 dtype casting
  • Odd-circumference cylinders

Algorithm Tutorials

Algorithms

• DMRG
  • Background
  • Configuration
  • Example – Heisenberg chain
  • Result object
  • MPO construction
  • Example – 2D Heisenberg cylinder
  • Label conventions
• iDMRG
  • Background
  • Configuration
  • Example – Heisenberg chain
  • Example – Infinite cylinder
  • Result object
  • MPO construction
• TRG
  • Background
  • Configuration
  • Example – 2D Ising model
  • Helper functions
  • Convergence
• HOTRG
  • Background
  • Configuration
  • Example – 2D Ising model
  • TRG vs HOTRG
  • Direction order
• iPEPS
  • Background
  • Configuration
  • Example – 2D Heisenberg model
  • Result
  • CTMEnvironment
  • Using CTM standalone
  • 2-site checkerboard unit cell
• AD-Based iPEPS Excitations
  • Stable AD Infrastructure
  • AD Ground State Optimization
  • Excitation Spectrum
  • References
• AutoMPO
  • Background
  • Class-based API
  • Functional API
  • Built-in operators
  • HamiltonianTerm

Tools

Tools

• Benchmarks
  • Quick start
  • CLI reference
  • Algorithms and sizes
  • Output formats
  • How timing works
  • Backend notes
  • File layout

Reference

API Reference

• API Reference
  • Core – Symmetries, Indices, and Tensors
  • Contraction Engine
  • Tensor Network
  • Algorithms

Additional Resources

Notes

• Contraction Semantics