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arXiv:2607.26132

Quantum Phase Diagram of the $2+1$D Untruncated SU$(2)$ Lattice Gauge Theory with Dynamical Fermions

Gabriel Rouxinol, Julian Bender, Patrick Emonts, Michele Grossi, Jad C. Halimeh

hep-latcond-mat.quant-gascond-mat.str-elhep-phquant-phSubmitted Jul 28, 2026• Announced Jul 30, 2026
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Abstract

Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU$(2)$ gauge field without truncation, we determine the ground-state behavior of the SU$(2)$ lattice gauge theory with staggered fermions on an $L\times L$ square lattice. Treating the magnetic and electric couplings $λ$ and $g^2$ independently, we find a magnetic-flux transition at $λ^\ast=-0.040\pm 0.005$, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line $λ=4/g^2$, for $L=4,6,8$, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.

Comments
8+3 pages, 3+3 figures

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APS March Meeting Abstracts•Dec 22, 2017•0 citations
Quantum Phase Diagram of the 2+12+12+1D Untruncated SU(2)(2)(2) Lattice Gauge Theory with Dynamical Fermions
Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU(2)(2)(2) gauge field without truncation, we determine the ground-state behavior of the SU(2)(2)(2) lattice gauge theory with staggered fermions on an L×LL\times LL×L square lattice. Treating the magnetic and electric couplings λλλ and g2g^2g2 independently, we find a magnetic-flux transition at λ∗=−0.040±0.005λ^\ast=-0.040\pm 0.005λ∗=−0.040±0.005, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line λ=4/g2λ=4/g^2λ=4/g2, for L=4,6,8L=4,6,8L=4,6,8, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.
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