# Neural-network quantum state study of the long-range antiferromagnetic Ising chain

arXiv: https://arxiv.org/abs/2308.09709 · HTML: https://mlsanity.com/paper/2308.09709/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 87 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Equivalence of restricted Boltzmann machines and tensor network states](https://mlsanity.com/paper/1701.04831/) (2017)
- [Neural tensor contractions and the expressive power of deep neural quantum states](https://mlsanity.com/paper/2103.10293/) (2021)
- [Neural network wave functions and the sign problem](https://mlsanity.com/paper/2002.04613/) (2020)

## Abstract (arXiv)

We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent αLR, while the other critical exponents examined are very close to the SR Ising exponents regardless of αLR examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for αLR < 2, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as αLR decreases, although a precise breakdown threshold is yet to be determined.