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Deep learning lattice gauge theories

May 23, 2024
62 pages
Published in:
  • Phys.Rev.B 110 (2024) 16, 165133
  • Published: Oct 15, 2024
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Abstract: (APS)
Monte Carlo methods have led to profound insights into the strong-coupling behavior 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 ZN 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 Z2, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the Z3 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.
  • phase: topological
  • critical phenomena: confinement
  • invariance: gauge
  • hadron: mass
  • lattice field theory
  • neural network
  • quantum state
  • Monte Carlo
  • universality
  • ground state