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

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Main Authors: Spriggs, Thomas, Greplova, Eliska, Carrasquilla, Juan, Nys, Jannes
Format: Preprint
Published: 2025
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author Spriggs, Thomas
Greplova, Eliska
Carrasquilla, Juan
Nys, Jannes
author_facet Spriggs, Thomas
Greplova, Eliska
Carrasquilla, Juan
Nys, Jannes
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_12323
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D
Spriggs, Thomas
Greplova, Eliska
Carrasquilla, Juan
Nys, Jannes
High Energy Physics - Lattice
Computational Physics
Quantum Physics
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.
title Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D
topic High Energy Physics - Lattice
Computational Physics
Quantum Physics
url https://arxiv.org/abs/2509.12323