Deep learning lattice gauge theories
<|reference_start|>Deep learning lattice gauge theories: Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.<|reference_end|>
@article{apte2024deep,
    title={Deep learning lattice gauge theories},
    author={Anuj Apte, Anthony Ashmore, Clay Cordova, Tzu-Chen Huang},
    journal={arXiv preprint arXiv:2405.14830},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14830},
    primaryClass={hep-lat cond-mat.dis-nn cond-mat.str-el cs.LG hep-th}
}