Neural-network Quantum State Of Transverse-field Ising Model

We use the neural network quantum states to represent the wave function of one-dimensional and two-dimensional transverse field Ising model.This wave function are equivalent to a mapping from the spin configuration space to the complex domain deter-mined by the network parameters.That is to say,when we input a spin configuration to the wave function,it will feed back a complex number.We use unsupervised machine learning to find the ground state wave function.Specifically,we use Stochastic Recon-figuration(SR)method to adjust the network parameters of the wave function,so that the wave function keeps approaching the ground state.At the same time,We provide for this SR method an understanding basing on least action principle and information geometries.With this quantum state,we calculate key observables of the system based the importance sampling method,they include the energy,correlation function,corre-lation length,magnetic moment and susceptibility.We have explored the relationship between these key observables and the strength of the transverse field.Our results are in good agreement with those in the literature.Especially,the calculation of entanglement entropy is different from these observables,because the operation of density matrix p will be faced in the calculation process,so that it is impossible to use simple importance sam-pling method to calculate their statistical average.We provide a feasible approximation method for calculating entanglement entropy,and their one-dimensional results are in good agreement with the existing analytical results.The two-dimensional results are also similar to the existing mathematical results for quantum phase transition.In addition,we also discussed the influence of network parameter ? on the calculation accuracy.The results show that the value of ? has little effect on the calculation accuracy.