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

Research Approach

This paper investigates the ground-state properties of 2+1D SU(2) lattice gauge theory coupled to staggered fermions. Unlike traditional Euclidean Monte Carlo methods, which often struggle with the sign problem, the authors employ a Hamiltonian-based variational Monte Carlo approach. This method works directly in the magnetic basis and retains the full, untruncated SU(2) gauge group. The variational ansatz combines a neural-network-based gauge wave function with a gauge-covariant Gaussian fermionic state, allowing for the simultaneous optimization of both gauge and matter sectors.

Magnetic-Flux Transition

By treating the magnetic coupling (lambda) and electric coupling (g^2) as independent parameters, the researchers identified a magnetic-flux transition at lambda = -0.040 +/- 0.005. This transition is characterized by a shift between a pi-flux sector and a unity-flux sector. The authors observed hysteresis in the plaquette expectation values near this point, which serves as evidence for a phase transition. Notably, the transition point remains stable even as the electric coupling is varied, suggesting that electric-field fluctuations primarily broaden the gauge distribution without shifting the underlying magnetic-flux competition.

Gauge-Matter Delocalization

Along the physical coupling line (lambda = 4/g^2), the system exhibits a crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. This transition is accompanied by a delocalization of matter: as the electric penalty for flux fluctuations decreases, the fermions move away from their localized Neel-state reference. This evolution is confirmed by consistent signatures across multiple observables, including the chiral condensate, the local color density, and gauge-invariant Wilson-line meson correlators.

This work provides a unified physical picture of how non-Abelian gauge theories behave when dynamical matter is present. By successfully implementing an untruncated variational framework, the authors open a path to studying regimes—such as those with finite chemical potential or topological terms—that are typically inaccessible to standard lattice techniques. This approach offers a powerful tool for exploring confinement, gauge-assisted matter dynamics, and strongly correlated quantum systems.