Code and scripts for ``Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory''

In the Hamiltonian limit, i.e. at vanishing temporal lattice spacing a_t, the path integral approach in the Lagrangian formalism reproduces the results of the Hamiltonian theory. In this work, we numerically calculate the Hamiltonian limit of a U(1) gauge theory in (2+1) dimensions.

This is achieved by Monte Carlo simulations in the Lagrangian formalism with lattices that are anisotropic in the time direction. For each ensemble, we determine the ratio between the temporal and spatial scale with the static quark potential and extrapolate to a_t to 0. Our results are compared with the data from Hamiltonian simulations at small volumes, showing agreement within <2 sigma.