Probing quantum critical phase from neural network wavefunction

TL;DR

This paper demonstrates that neural network quantum Monte Carlo methods can effectively study quantum phase transitions in 1D systems, capturing critical behaviors and phase breakdowns with high accuracy.

Contribution

It extends neural network quantum Monte Carlo techniques to analyze quantum critical phases in 1D systems, revealing new phase behaviors and demonstrating neural networks' capability in complex quantum simulations.

Findings

Neural networks can capture quantum critical behavior of TLL.

Identification of breakdown of TLL and emergence of Fermi liquid.

High-energy orbitals influence phase transitions.

Abstract

One-dimensional (1D) systems and models provide a versatile platform for emergent phenomena induced by strong electron correlation. In this work, we extend the newly developed real space neural network quantum Monte Carlo methods to study the quantum phase transition of electronic and magnetic properties. Hydrogen chains of different interatomic distances are explored systematically with both open and periodic boundary conditions, and fully correlated ground state many-body wavefunction is achieved via unsupervised training of neural networks. We demonstrate for the first time that neural networks are capable of capturing the quantum critical behavior of Tomonaga- Luttinger liquid (TLL), which is known to dominate 1D quantum systems. Moreover, we reveal the breakdown of TLL phase and the emergence of a Fermi liquid behavior, evidenced by abrupt changes in the spin structure and the momentum distribution. Such behavior is absent in commonly studied 1D lattice models and is likely due to the involvement of high-energy orbitals of hydrogen atoms. Our work highlights the powerfulness of neural networks for representing complex quantum phases.