Deep learning lattice gauge theories

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.

Updated to match journal version; LGE-CNN diagram corrected

References in corpus (49)

• Anyons in an exactly solved model and beyond
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Generalized Global Symmetries
• The Variational Quantum Eigensolver: a review of methods and best practices
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Ab-initio Determination of Light Hadron Masses
• Precision Islands in the Ising and $O(N)$ Models
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Quantum Entanglement in Neural Network States
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Superconductors are topologically ordered
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Equivalence of restricted Boltzmann machines and tensor network states
• Low-energy effective theory of the toric code model in a parallel field
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Neural tensor contractions and the expressive power of deep neural quantum states
• Neural network wave functions and the sign problem
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Empowering deep neural quantum states through efficient optimization
• Breakdown of a perturbed Z_N topological phase
• Renyi Entropy of the Interacting Fermi Liquid
• The string tension from smeared Wilson loops at large N
• Qudit surface codes and gauge theory with finite cyclic groups
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Neural-network quantum states for many-body physics
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Purifying Deep Boltzmann Machines for Thermal Quantum States
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• Gauge equivariant neural networks for quantum lattice gauge theories
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• Entanglement entropy from non-equilibrium Monte Carlo simulations
• On the spectrum and string tension of U(1) lattice gauge theory in 2+1 dimensions
• Generalization capabilities of translationally equivariant neural networks
• Efficient evaluation of high-order moments and cumulants in tensor network states
• 3D Ising Model: a view from the Conformal Bootstrap Island
• Duality transformations and the entanglement entropy of gauge theories
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Applications of Lattice Gauge Equivariant Neural Networks
• Wegner-Wilson loops in string nets
• Preserving gauge invariance in neural networks

Cited by in corpus (4)

• Towards constraining QCD phase transitions in neutron star interiors: Bayesian Inference with TOV linear response analysis
• Intertwined order of generalized global symmetries
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter