GrassmannTensorNetworks

GrassmannTensorNetworks is a Julia package for Grassmann tensor networks with Z2 parity structure. It includes core tensor algebra, decomposition routines with AD support, and higher-level PEPS / CTMRG utilities.

Installation

using Pkg
Pkg.add("GrassmannTensorNetworks")
using GrassmannTensorNetworks

For local development:

using Pkg
Pkg.activate(".")
Pkg.instantiate()
using GrassmannTensorNetworks

Package layout

The package currently has three layers:

• src/: core Grassmann tensor types and tensor algebra.
• auxiliary/: PEPS ansatz, model helpers, and utility functions.
• algorithms/: simple update and CTMRG routines built on top of the core package API.

Documentation

The repository docs live in docs/. They cover:

• the Grassmann type and structural helpers,
• tensor operations and decompositions,
• AD support,
• higher-level PEPS / CTMRG utilities.

Development

using Pkg
Pkg.activate(".")
Pkg.instantiate()
Pkg.test()

The ChainRules/Zygote rules are loaded from ext/GrassmannChainRulesCoreExt when ChainRulesCore and Zygote are available. CUDA support is loaded from ext/GrassmannCUDAExt when CUDA is available.

Examples

• examples/Spinless_Fermion_2D_Square_AD_nested/Spinless_Fermion_2D_Square_AD_nested.jl: Grassmann nested-CTMRG optimization for the square-lattice spinless fermion.

Run the nested example from the repository root with, for example:

$env:NESTED_CHI = "4"
$env:NESTED_SEED = "1234"
$env:NESTED_VERBOSITY = "0"
julia --project=. examples/Spinless_Fermion_2D_Square_AD_nested/Spinless_Fermion_2D_Square_AD_nested.jl

The executable configuration fixes D = 2, ctmrg_iter = 20, and ad_iter = 20. The requested acceptance runs set NESTED_CHI to 4, 8, and 12 with a common seed. Their finite, error-free energies should show an overall trend toward the exact value -6.170521774015... as chi increases; there is no fixed one-percent error threshold at chi = 12.