NonLocalCorrelationTutorial

A light, hands-on set of notes and notebooks for my tutorial at TIFR on non-local correlations and quantum many-body numerics.

• School page: https://sites.google.com/view/nonlocalcorrelationsquantumsys/homepage
• Main theme: tensor-network algorithms for ground-state search, with a special focus on DMRG

Tensor networks: because the full Hilbert space is very large, but our patience is not.

What’s in here

This repository currently contains two Jupyter notebooks (using Julia + ITensors.jl) that build intuition and practical workflow:

1. 1D transverse-field Ising (TFI) chain DMRG

   • Define a quantum wavefunction and spin-chain Hamiltonians as MPS and MPO.
   • Use DMRG to find ground states.
   • Explore phases and the phase transition by scanning parameters.
   • Observe the scaling at criticality of bond dimensions for systems that has large correlation lengths.

2. 2D system via snake-DMRG

   • Map a 2D lattice to a 1D “snake” ordering.
   • Watch the bond dimension _grow and grow and GROW with system size.

3. 1D TFI chain ground state search and time evolution using neural network Quantum States (NNQS)

   • This notebook is written in Python, and has the theory and implementation of ground state search, stochastic reconfiguration, and time evolution of 1D TFI models. It uses NetKet to perform the simulations.

Getting started

Clone this repo to your local machine:

git clone https://github.com/SUTD-MDQS/NonLocalCorrelationTutorial.git

1. Installing Jupyter

If you don't have JupyterLab (or Jupyter Notebook) installed, you can do so via pip or conda. Prerequisites: pip or conda commands installed in your terminal.

• Using conda:

  conda install -c conda-forge jupyterlab

• Using pip:

  pip install jupyterlab

(I recommend against running the notebooks via VS Code Jupyter extension. Occasionally the notebook formatting gets complicated.)

2. Installing Julia

If not installed, you can install the official Julia language for your OS from here. Alternatively, you can also run these terminal commands based on your OS:

• macOS:

brew install julia

• Linux:

curl -fsSL https://install.julialang.org | sh

• Windows (requires Microsoft Store):

winget install --name Julia --id 9NJNWW8PVKMN -e -s msstore

3. Setting up Julia venv

This repo ships with a pinned Julia environment (Project.toml) to keep the packages we need consistent across laptops. Prerequisites: Julia v1.10 or higher installed and available in your terminal. From the repo root, run:

julia --project=. -e 'using Pkg; Pkg.instantiate(); Pkg.precompile()'

4. Register the Julia kernel with Jupyter

To use the Julia environment in Jupyter notebooks, you need to register a new kernel. From the repo root, run:

julia --project=. -e 'using IJulia; IJulia.installkernel("Julia (NonLocalCorrelationTutorial)", env=Dict("JULIA_PROJECT"=>pwd()))'

5. Running the notebooks

• Open JupyterLab/Notebook in the folder containing the notebooks.
• Select the Julia (NonLocalCorrelationTutorial) kernel for the notebooks.

If everything ran without errors, you should now be ready to run the notebooks (whew!).

Laptop fan attempting lift-off?
Try reducing the system sizes (your specs might not be sufficient).

License

Unless stated otherwise in individual notebooks, feel free to use this material for learning and teaching, with attribution.