Repesentation of general spin-$S$ systems using a Restricted Boltzmann Machine with Softmax Regression

TL;DR

This paper introduces a novel SRBM-based method for representing general spin systems, demonstrating improved efficiency and accuracy in approximating many-body wave functions compared to traditional methods.

Contribution

The paper presents a new SRBM approach with Softmax Regression for spin systems, showing enhanced efficiency and accuracy in wave function representation.

Findings

SRBM achieves accurate wave functions for spin-1/2 systems.

Method's accuracy improves with more hidden units.

Results agree well with Exact Diagonalization and DMRG.

Abstract

Here, we propose a novel method for representation of general spin systems using Restricted Boltzmann Machine with Softmax Regression (SRBM) that follows the probability distribution of the training data. SRBM training is performed using stochastic reconfiguration method to find approximate representation of many body wave functions. We have shown that proposed SRBM technique performs very well and achieves the trial wave function, in a numerically more efficient way, which is in good agreement with the theoretical prediction. We demonstrated that the prediction of the trial wave function through SRBM becomes more accurate as one increases the number of hidden units. We evaluated the accuracy of our method by studying the spin-1/2 quantum systems with softmax RBM which shows good accordance with the Exact Diagonalization(ED). We have also compared the energies of spin chains of a few spin multiplicities($1, 3/2$ and $2$) with ED and DMRG results.