Matrix Models with Netket

Find the ground state of matrix models using variational neural states in netket.

This repository depends on the netket library (v3.0).

We included a notebook based on the nice Ground-State: Ising model tutorial by Filippo Vicentini at this link.

Install

The documentation page for netket suggests to create a python virtual environment and then use pip to install the library. In this repository we work with the serial CPU version of netket and we create a minimal virtual environment using conda based on the environment.yml file:

conda env create -f environment.yml
conda activate netket

Note: netket is installed in the environment using pip. The installation is for a single CPU.

• If you need a MPI installation use environment_mpi.yml but me mindful that the MPI dependency mpi4py is installed via conda, despite all the warnings from the NetKet team).

• If you need a GPU installation use environment_gpu.yml which is installing JAX with GPU support before installing netket.

Notebooks

The MatrixModel.ipynb notebooks is an introduction to using netket for finding the variational ground state of a bosonic matrix model using a neural state ansatz and a variational Monte Carlo sampler for states in a Fock basis. The simpler case of zero coupling constant is shown in HarmonicOscillators.ipynb.

You can run the notebooks on Google Colaboratory:

The variational energy of the ground state as a function of the optimization process is shown below for two neural state ansatz