Quantum many-body ground-state optimization by VMC of RBM

Optimizing GS energy of quantum many-body system by VMC with RBM as trial function, based on Carleo & Troyer, Science 355, 602 (2017). Here, we demonstrate the method at the antiferro Heisenberg model and J1-J2 Heisenberg model in one dimension. The description of each codes are given as follows.

main.ipynb

The main execution file of the scheme.

Auxiliary files

ExactWaveFunc_(model).py: Exact wave function and GS energy of finite-size system.

Hamiltonian_(model).py: Defining the Hamiltonian of finite-size system.

RBM_(model).py: Class file of RBM for the model. Derivatives for RBM parameters, local energy, and unsampled (analytical) wave function amplitudes are computed.

RealSamplingTools.py: Gibbs sampler from the RBM by the alternate sampling method.

MetropolisSamplingTools.py: Sampler from the RBM by the ordinary single-flip algorithm based on Metropolis-Hastings rule.

Real/ComplexWFtools.py: Auxiliary functions to compare the exact and numerically optimized wave function.

VMC_(model).py: VMC scheme. Sampling the spin configuration, calculating the gradients, and updating RBM parameters.

plottools_(model).py: Save, load, and name the result.