# Neural-network Quantum State of Transverse-field Ising Model

## TL;DR

This paper constructs a neural-network quantum state for the transverse-field Ising model using unsupervised learning and stochastic reconfiguration, enabling efficient calculation of key physical observables and entanglement entropy.

## Contribution

It introduces a novel high-efficiency neural network approach combined with an understanding from information geometry to model the TFIM ground state.

## Key findings

- Accurately computes energy, correlation functions, and magnetic properties.
- Successfully calculates entanglement entropy consistent with previous studies.
- Provides a new efficient method for quantum state representation.

## Abstract

Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.