🤖 AI Summary
Sign problems and the intractability of real-time dynamics pose fundamental challenges for lattice gauge theory simulations. Method: We introduce a gauge-invariant neural network quantum state ansatz, incorporating transfer learning and group-representation-theoretic architectural constraints, to enable efficient variational Monte Carlo optimization of ground states in (2+1)D ℤ₂ and ℤ₃ gauge theories. Contribution/Results: This is the first application of such an approach to phase transition studies in these models: we precisely identify the ℤ₂ model’s continuous phase transition as belonging to the Ising universality class—confirmed by critical exponents in excellent agreement with theory—and locate the weakly first-order confinement transition in the ℤ₃ model. The method circumvents the sign problem, supports real-time evolution, and exhibits favorable scalability. It establishes the first machine-learning-based computational paradigm for strongly coupled gauge systems that is both sign-problem-free and rigorously gauge-conserving.
📝 Abstract
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.