Related papers: Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D

Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D

URL: http://arxiv.org/abs/2509.12323v1
Date: Mon, 15 Sep 2025 18:00:17 GMT
Title: Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D
Authors: Thomas Spriggs, Eliska Greplova, Juan Carrasquilla, Jannes Nys,
Abstract summary: We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation.<n>We learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions.<n>Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems.
Score: 0.7999703756441757
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of $SU(2)$ equivariant neural networks alongside an $SU(2)$ invariant, physics-inspired ansatz, we learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to $SU(N)$. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

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