Large scale GPU study of the confinement transition in U(1) lattice gauge theories

U(1) lattice gauge theories can emerge from condensed matter systems, such as quantum spin ice in 3 spatial dimensions. In such systems, interactions between emergent charges and photons are controlled by a coupling analogous to the fine structure constant in the standard model of QED. We study the deconfinement transition in the compact pure U(1) gauge theory in (3+1) dimensions using a dual integer-plaquette representation. We first provide evidence supporting previous studies of the cosine potential with significantly larger scale Monte Carlo simulations on system sizes up to $V=128^4$. We confirm that the deconfinement transition is weakly first-order with a small dimensionless latent heat, and observe hysteresis and phase coexistence. We then introduce a new family of plaquette potentials parameterized by positive real number $\lambda$. $\lambda=2$ approximates the cosine potential in the large coupling limit and is commonly known as the Villain potential. Driving $\lambda\rightarrow\infty$ weakens the transition and minimizes the latent heat. We argue that this limit maximizes the renormalized fine structure constant at the transition.