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 the fully correlated ground-state many-body wavefunction is achieved via unsupervised training of neural networks. We demonstrate 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 the 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 power of neural networks for representing complex quantum phases.

Close

PrevNext

View figure in article

• Quantum phase transitions
• 1-dimensional systems
• Electron-correlation calculations
• Machine learning
• Many-body techniques
• Quantum Monte Carlo