Neural Quantum State Study of Fracton Models

TL;DR

This paper introduces neural quantum states as effective tools for studying phase transitions in complex three-dimensional fracton models, demonstrating their accuracy and potential in analyzing highly entangled quantum systems.

Contribution

The authors develop exact neural quantum state parametrizations for key fracton models and adapt them to study phase transitions, showcasing the method's effectiveness in 3D quantum systems.

Findings

Reproduced known phase transitions in fracton models.

Simulated systems of up to 512 qubits with high accuracy.

Demonstrated neural quantum states' potential for complex 3D quantum problems.

Abstract

Fracton models host unconventional topological orders in three and higher dimensions and provide promising candidates for quantum memory platforms. Understanding their robustness against quantum fluctuations is an important task but also poses great challenges due to the lack of efficient numerical tools. In this work, we establish neural quantum states (NQS) as new tools to study phase transitions in these models. Exact and efficient parametrizations are derived for three prototypical fracton codes -- the checkerboard and X-cube model, as well as Haah's code -- both in terms of a restricted Boltzmann machine (RBM) and a correlation-enhanced RBM. We then adapt the correlation-enhanced RBM architecture to a perturbed checkerboard model and reveal its strong first-order phase transition between the fracton phase and a trivial field-polarizing phase. To this end, we simulate this highly entangled system on lattices of up to 512 qubits with high accuracy, representing a cutting-edge application of variational neural-network methods. In addition, we reproduce the phase transition of the X-cube model previously obtained with quantum Monte Carlo and high-order series expansion methods. Our work demonstrates the remarkable potential of NQS in studying complicated three-dimensional problems and highlights physics-oriented constructions of NQS architectures.