GrassmannTN 1.4.0

GrassmannTN is a python package that aims to simplify the coding involving Grassmann tensor network. The goal is to make the coding as convenient as when you use other standard packages like numpy or scipy. All the sign factors are computed automatically without explicit user inputs. If you have further questions about the package and how to use it, please contact me via ayosp-at-phys.sc.niigata-u.ac.jp

Package structure

• grassmanntn (main module): contains most of the features.

• grassmanntn.param: contains technical functions such as the sign factor \(\sigma_I\), the parity \(p(I)\) or the encoder-switching function \(\varepsilon(I)\).

• grassmann.arith: a new module added in v 1.3.0 to help the user build the initial tensor directly from the fermionic action/Hamiltonian. Symbolic expression is supported.

Useful links

• GitHub

• PyPI

• full paper

• arXiv

Prerequisites

• numpy

• sparse

• opt_einsum

• sympy

Installation

Installation via PyPI

pip install grassmanntn

Once the package is installed, download example.py and try running it with

python3 example.py --show_progress

An example code of a one-flavor two-dimensional \(\mathbb{Z}_2\) gauge theory should be able to run.

Contents:

• Release notes
  • v 1.4.0
  • v 1.3.5
  • v 1.3.4
  • v 1.3.3
  • v 1.3.2
  • v 1.3.1
  • v 1.3.0
  • v 1.2.3
• Package settings
• Basic examples
  • Initialization
  • Contraction
  • Tensor decompositions
  • Hermitian conjugation
• Advanced example: 2D Schwinger model
  • Introduction
  • Initial tensor preparation
  • Initial tensor compression
  • Coarse-graining procedures
• grassmanntn (main module)
  • dense and sparse
  • block
  • einsum()
  • join_legs() and split_legs()
  • hconjugate()
  • svd() and eig()
  • power()
  • sqrt()
  • random()
• grassmanntn.param
  • gparity()
  • sgn()
  • encoder()
• grassmanntn.arith
  • grassmann_number
  • berezin_measure
  • set_anticommutative
  • get_coeff()
  • exp()