Pierpaolo Fontana - Università di Trieste

Renormalized dual basis for scalable simulations of higher dimensional lattice gauge theories

We present the Renormalized Dual Basis (RDB), a scalable and resource-efficient framework for the classical and quantum simulation of lattice gauge theories (LGTs) with continuous gauge groups in higher dimensions. The method combines a dual formulation of the theory with a local optimization of the gauge basis, obtained from the solution of the single-plaquette problem, enabling an efficient truncation of the infinite-dimensional Hilbert space of gauge degrees of freedom. We apply the approach to both Abelian and non-Abelian LGTs in two spatial dimensions, focusing on compact quantum electrodynamics (cQED) and pure SU(2) gauge theories. For small lattices with periodic boundary conditions in the pure gauge case, and open boundary conditions in the presence of fermionic matter, we determine the ground state properties of the theory and compute gauge-invariant observables such as the plaquette expectation value. Compared to standard truncation schemes, the RDB achieves improved accuracy while requiring significantly fewer local basis states across all coupling regimes. To assess the scalability of the method, we further investigate larger lattice systems using tensor network algorithms. These results demonstrate that the RDB remains efficient as the system size increases, without a dramatic growth in computational resources.