Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions

Gauge theories underpin much of modern physics, from the Standard Model to effective descriptions of strongly interacting systems. While quantum chromodynamics is perturbative at high energies, nonperturbative tools are required in the low-energy regime. Lattice gauge theory provides a gauge-invariant regularization well suited for this purpose. By using Euclidean Monte Carlo simulations, this formulation has enabled major progress. Yet important regimes — such as finite-density fermionic systems and real-time dynamics — remain difficult due to the sign problem and the Euclidean nature of standard algorithms. These challenges have motivated alternative approaches, including Hamiltonian formulations amenable to quantum simulation and variational methods. Among the most powerful classical variational techniques are tensor networks. In this talk, I will give a short introduction into tensor networks and introduce a specific Ansatz, Gauged Gaussian Projected Entangled Pair States (GGPEPS). GGPEPS are gauge-invariant tensor-network, that allow efficient contraction in higher spatial dimension, and avoid the sign problem due to a variational Monte Carlo procedure. I will outline their construction, discuss key analytical features, and demonstrate their numerical performance on a (2+1)d Z2 lattice gauge theory with dynamical fermionic matter.