Deep learning lattice gauge theories
This work addresses fundamental problems in theoretical physics for researchers studying quantum field theories, offering a promising alternative to Monte Carlo methods, though it is incremental as it builds on existing neural network quantum state approaches.
The authors tackled the challenges of simulating lattice gauge theories, such as the sign problem and real-time dynamics, by using gauge-invariant neural network quantum states to accurately compute ground states and phase transitions in Z_N theories, achieving excellent agreement with existing numerics for critical exponents in Z_2 and identifying a first-order transition in Z_3.
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.